Given the Number 25,193,168,000, Calculate (Find) All the Factors (All the Divisors) of the Number 25,193,168,000 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 25,193,168,000

1. Carry out the prime factorization of the number 25,193,168,000:

The prime factorization of a number: finding the prime numbers that multiply together to make that number.


25,193,168,000 = 27 × 53 × 7 × 113 × 132
25,193,168,000 is not a prime number but a composite one.


* Prime number: a natural number that is divisible (divided evenly) only by 1 and itself. A prime number has exactly two factors: 1 and the number itself.
* Composite number: a natural number that has at least one other factor than 1 and itself.


2. Multiply the prime factors of the number 25,193,168,000

Multiply the prime factors involved in the prime factorization of the number in all their unique combinations, that give different results.


Also consider the exponents of these prime factors.

Also add 1 to the list of factors (divisors). All the numbers are divisible by 1.


All the factors (divisors) are listed below - in ascending order

The list of factors (divisors):

neither prime nor composite = 1
prime factor = 2
22 = 4
prime factor = 5
prime factor = 7
23 = 8
2 × 5 = 10
prime factor = 11
prime factor = 13
2 × 7 = 14
24 = 16
22 × 5 = 20
2 × 11 = 22
52 = 25
2 × 13 = 26
22 × 7 = 28
25 = 32
5 × 7 = 35
23 × 5 = 40
22 × 11 = 44
2 × 52 = 50
22 × 13 = 52
5 × 11 = 55
23 × 7 = 56
26 = 64
5 × 13 = 65
2 × 5 × 7 = 70
7 × 11 = 77
24 × 5 = 80
23 × 11 = 88
7 × 13 = 91
22 × 52 = 100
23 × 13 = 104
2 × 5 × 11 = 110
24 × 7 = 112
112 = 121
53 = 125
27 = 128
2 × 5 × 13 = 130
22 × 5 × 7 = 140
11 × 13 = 143
2 × 7 × 11 = 154
25 × 5 = 160
132 = 169
52 × 7 = 175
24 × 11 = 176
2 × 7 × 13 = 182
23 × 52 = 200
24 × 13 = 208
22 × 5 × 11 = 220
25 × 7 = 224
2 × 112 = 242
2 × 53 = 250
22 × 5 × 13 = 260
52 × 11 = 275
23 × 5 × 7 = 280
2 × 11 × 13 = 286
22 × 7 × 11 = 308
26 × 5 = 320
52 × 13 = 325
2 × 132 = 338
2 × 52 × 7 = 350
25 × 11 = 352
22 × 7 × 13 = 364
5 × 7 × 11 = 385
24 × 52 = 400
25 × 13 = 416
23 × 5 × 11 = 440
26 × 7 = 448
5 × 7 × 13 = 455
22 × 112 = 484
22 × 53 = 500
23 × 5 × 13 = 520
2 × 52 × 11 = 550
24 × 5 × 7 = 560
22 × 11 × 13 = 572
5 × 112 = 605
23 × 7 × 11 = 616
27 × 5 = 640
2 × 52 × 13 = 650
22 × 132 = 676
22 × 52 × 7 = 700
26 × 11 = 704
5 × 11 × 13 = 715
23 × 7 × 13 = 728
2 × 5 × 7 × 11 = 770
25 × 52 = 800
26 × 13 = 832
5 × 132 = 845
7 × 112 = 847
53 × 7 = 875
24 × 5 × 11 = 880
27 × 7 = 896
2 × 5 × 7 × 13 = 910
23 × 112 = 968
23 × 53 = 1,000
7 × 11 × 13 = 1,001
24 × 5 × 13 = 1,040
22 × 52 × 11 = 1,100
25 × 5 × 7 = 1,120
23 × 11 × 13 = 1,144
7 × 132 = 1,183
2 × 5 × 112 = 1,210
24 × 7 × 11 = 1,232
22 × 52 × 13 = 1,300
113 = 1,331
23 × 132 = 1,352
53 × 11 = 1,375
23 × 52 × 7 = 1,400
27 × 11 = 1,408
2 × 5 × 11 × 13 = 1,430
24 × 7 × 13 = 1,456
22 × 5 × 7 × 11 = 1,540
112 × 13 = 1,573
26 × 52 = 1,600
53 × 13 = 1,625
27 × 13 = 1,664
2 × 5 × 132 = 1,690
2 × 7 × 112 = 1,694
2 × 53 × 7 = 1,750
25 × 5 × 11 = 1,760
22 × 5 × 7 × 13 = 1,820
11 × 132 = 1,859
52 × 7 × 11 = 1,925
24 × 112 = 1,936
24 × 53 = 2,000
2 × 7 × 11 × 13 = 2,002
25 × 5 × 13 = 2,080
23 × 52 × 11 = 2,200
26 × 5 × 7 = 2,240
52 × 7 × 13 = 2,275
24 × 11 × 13 = 2,288
2 × 7 × 132 = 2,366
22 × 5 × 112 = 2,420
25 × 7 × 11 = 2,464
23 × 52 × 13 = 2,600
2 × 113 = 2,662
24 × 132 = 2,704
2 × 53 × 11 = 2,750
24 × 52 × 7 = 2,800
22 × 5 × 11 × 13 = 2,860
25 × 7 × 13 = 2,912
52 × 112 = 3,025
23 × 5 × 7 × 11 = 3,080
2 × 112 × 13 = 3,146
27 × 52 = 3,200
2 × 53 × 13 = 3,250
22 × 5 × 132 = 3,380
22 × 7 × 112 = 3,388
22 × 53 × 7 = 3,500
26 × 5 × 11 = 3,520
52 × 11 × 13 = 3,575
23 × 5 × 7 × 13 = 3,640
2 × 11 × 132 = 3,718
2 × 52 × 7 × 11 = 3,850
25 × 112 = 3,872
25 × 53 = 4,000
22 × 7 × 11 × 13 = 4,004
26 × 5 × 13 = 4,160
52 × 132 = 4,225
5 × 7 × 112 = 4,235
24 × 52 × 11 = 4,400
27 × 5 × 7 = 4,480
2 × 52 × 7 × 13 = 4,550
25 × 11 × 13 = 4,576
22 × 7 × 132 = 4,732
23 × 5 × 112 = 4,840
26 × 7 × 11 = 4,928
5 × 7 × 11 × 13 = 5,005
24 × 52 × 13 = 5,200
22 × 113 = 5,324
25 × 132 = 5,408
22 × 53 × 11 = 5,500
25 × 52 × 7 = 5,600
23 × 5 × 11 × 13 = 5,720
26 × 7 × 13 = 5,824
5 × 7 × 132 = 5,915
2 × 52 × 112 = 6,050
24 × 5 × 7 × 11 = 6,160
22 × 112 × 13 = 6,292
22 × 53 × 13 = 6,500
5 × 113 = 6,655
23 × 5 × 132 = 6,760
23 × 7 × 112 = 6,776
23 × 53 × 7 = 7,000
27 × 5 × 11 = 7,040
2 × 52 × 11 × 13 = 7,150
24 × 5 × 7 × 13 = 7,280
22 × 11 × 132 = 7,436
22 × 52 × 7 × 11 = 7,700
26 × 112 = 7,744
5 × 112 × 13 = 7,865
26 × 53 = 8,000
23 × 7 × 11 × 13 = 8,008
27 × 5 × 13 = 8,320
2 × 52 × 132 = 8,450
2 × 5 × 7 × 112 = 8,470
25 × 52 × 11 = 8,800
22 × 52 × 7 × 13 = 9,100
26 × 11 × 13 = 9,152
5 × 11 × 132 = 9,295
7 × 113 = 9,317
23 × 7 × 132 = 9,464
53 × 7 × 11 = 9,625
24 × 5 × 112 = 9,680
27 × 7 × 11 = 9,856
2 × 5 × 7 × 11 × 13 = 10,010
25 × 52 × 13 = 10,400
23 × 113 = 10,648
26 × 132 = 10,816
23 × 53 × 11 = 11,000
7 × 112 × 13 = 11,011
26 × 52 × 7 = 11,200
53 × 7 × 13 = 11,375
24 × 5 × 11 × 13 = 11,440
27 × 7 × 13 = 11,648
2 × 5 × 7 × 132 = 11,830
22 × 52 × 112 = 12,100
25 × 5 × 7 × 11 = 12,320
23 × 112 × 13 = 12,584
23 × 53 × 13 = 13,000
7 × 11 × 132 = 13,013
2 × 5 × 113 = 13,310
24 × 5 × 132 = 13,520
24 × 7 × 112 = 13,552
24 × 53 × 7 = 14,000
22 × 52 × 11 × 13 = 14,300
25 × 5 × 7 × 13 = 14,560
23 × 11 × 132 = 14,872
53 × 112 = 15,125
23 × 52 × 7 × 11 = 15,400
27 × 112 = 15,488
2 × 5 × 112 × 13 = 15,730
27 × 53 = 16,000
24 × 7 × 11 × 13 = 16,016
22 × 52 × 132 = 16,900
22 × 5 × 7 × 112 = 16,940
113 × 13 = 17,303
26 × 52 × 11 = 17,600
53 × 11 × 13 = 17,875
23 × 52 × 7 × 13 = 18,200
27 × 11 × 13 = 18,304
2 × 5 × 11 × 132 = 18,590
2 × 7 × 113 = 18,634
24 × 7 × 132 = 18,928
2 × 53 × 7 × 11 = 19,250
25 × 5 × 112 = 19,360
22 × 5 × 7 × 11 × 13 = 20,020
112 × 132 = 20,449
26 × 52 × 13 = 20,800
53 × 132 = 21,125
52 × 7 × 112 = 21,175
24 × 113 = 21,296
27 × 132 = 21,632
24 × 53 × 11 = 22,000
2 × 7 × 112 × 13 = 22,022
27 × 52 × 7 = 22,400
2 × 53 × 7 × 13 = 22,750
25 × 5 × 11 × 13 = 22,880
22 × 5 × 7 × 132 = 23,660
23 × 52 × 112 = 24,200
26 × 5 × 7 × 11 = 24,640
52 × 7 × 11 × 13 = 25,025
24 × 112 × 13 = 25,168
24 × 53 × 13 = 26,000
2 × 7 × 11 × 132 = 26,026
22 × 5 × 113 = 26,620
25 × 5 × 132 = 27,040
25 × 7 × 112 = 27,104
25 × 53 × 7 = 28,000
23 × 52 × 11 × 13 = 28,600
26 × 5 × 7 × 13 = 29,120
52 × 7 × 132 = 29,575
24 × 11 × 132 = 29,744
2 × 53 × 112 = 30,250
24 × 52 × 7 × 11 = 30,800
22 × 5 × 112 × 13 = 31,460
25 × 7 × 11 × 13 = 32,032
52 × 113 = 33,275
23 × 52 × 132 = 33,800
23 × 5 × 7 × 112 = 33,880
2 × 113 × 13 = 34,606
27 × 52 × 11 = 35,200
2 × 53 × 11 × 13 = 35,750
24 × 52 × 7 × 13 = 36,400
22 × 5 × 11 × 132 = 37,180
22 × 7 × 113 = 37,268
25 × 7 × 132 = 37,856
22 × 53 × 7 × 11 = 38,500
26 × 5 × 112 = 38,720
52 × 112 × 13 = 39,325
23 × 5 × 7 × 11 × 13 = 40,040
2 × 112 × 132 = 40,898
27 × 52 × 13 = 41,600
2 × 53 × 132 = 42,250
2 × 52 × 7 × 112 = 42,350
25 × 113 = 42,592
25 × 53 × 11 = 44,000
22 × 7 × 112 × 13 = 44,044
22 × 53 × 7 × 13 = 45,500
26 × 5 × 11 × 13 = 45,760
52 × 11 × 132 = 46,475
5 × 7 × 113 = 46,585
23 × 5 × 7 × 132 = 47,320
24 × 52 × 112 = 48,400
27 × 5 × 7 × 11 = 49,280
2 × 52 × 7 × 11 × 13 = 50,050
25 × 112 × 13 = 50,336
25 × 53 × 13 = 52,000
22 × 7 × 11 × 132 = 52,052
23 × 5 × 113 = 53,240
26 × 5 × 132 = 54,080
26 × 7 × 112 = 54,208
5 × 7 × 112 × 13 = 55,055
26 × 53 × 7 = 56,000
24 × 52 × 11 × 13 = 57,200
27 × 5 × 7 × 13 = 58,240
2 × 52 × 7 × 132 = 59,150
25 × 11 × 132 = 59,488
22 × 53 × 112 = 60,500
25 × 52 × 7 × 11 = 61,600
23 × 5 × 112 × 13 = 62,920
26 × 7 × 11 × 13 = 64,064
5 × 7 × 11 × 132 = 65,065
2 × 52 × 113 = 66,550
24 × 52 × 132 = 67,600
24 × 5 × 7 × 112 = 67,760
22 × 113 × 13 = 69,212
22 × 53 × 11 × 13 = 71,500
25 × 52 × 7 × 13 = 72,800
23 × 5 × 11 × 132 = 74,360
23 × 7 × 113 = 74,536
26 × 7 × 132 = 75,712
23 × 53 × 7 × 11 = 77,000
27 × 5 × 112 = 77,440
2 × 52 × 112 × 13 = 78,650
24 × 5 × 7 × 11 × 13 = 80,080
22 × 112 × 132 = 81,796
22 × 53 × 132 = 84,500
22 × 52 × 7 × 112 = 84,700
26 × 113 = 85,184
5 × 113 × 13 = 86,515
26 × 53 × 11 = 88,000
23 × 7 × 112 × 13 = 88,088
23 × 53 × 7 × 13 = 91,000
27 × 5 × 11 × 13 = 91,520
2 × 52 × 11 × 132 = 92,950
2 × 5 × 7 × 113 = 93,170
24 × 5 × 7 × 132 = 94,640
25 × 52 × 112 = 96,800
22 × 52 × 7 × 11 × 13 = 100,100
26 × 112 × 13 = 100,672
5 × 112 × 132 = 102,245
26 × 53 × 13 = 104,000
23 × 7 × 11 × 132 = 104,104
53 × 7 × 112 = 105,875
24 × 5 × 113 = 106,480
27 × 5 × 132 = 108,160
27 × 7 × 112 = 108,416
2 × 5 × 7 × 112 × 13 = 110,110
27 × 53 × 7 = 112,000
25 × 52 × 11 × 13 = 114,400
22 × 52 × 7 × 132 = 118,300
26 × 11 × 132 = 118,976
23 × 53 × 112 = 121,000
7 × 113 × 13 = 121,121
26 × 52 × 7 × 11 = 123,200
53 × 7 × 11 × 13 = 125,125
24 × 5 × 112 × 13 = 125,840
27 × 7 × 11 × 13 = 128,128
2 × 5 × 7 × 11 × 132 = 130,130
22 × 52 × 113 = 133,100
25 × 52 × 132 = 135,200
25 × 5 × 7 × 112 = 135,520
23 × 113 × 13 = 138,424
23 × 53 × 11 × 13 = 143,000
7 × 112 × 132 = 143,143
26 × 52 × 7 × 13 = 145,600
53 × 7 × 132 = 147,875
24 × 5 × 11 × 132 = 148,720
24 × 7 × 113 = 149,072
27 × 7 × 132 = 151,424
24 × 53 × 7 × 11 = 154,000
22 × 52 × 112 × 13 = 157,300
This list continues below...

... This list continues from above
25 × 5 × 7 × 11 × 13 = 160,160
23 × 112 × 132 = 163,592
53 × 113 = 166,375
23 × 53 × 132 = 169,000
23 × 52 × 7 × 112 = 169,400
27 × 113 = 170,368
2 × 5 × 113 × 13 = 173,030
27 × 53 × 11 = 176,000
24 × 7 × 112 × 13 = 176,176
24 × 53 × 7 × 13 = 182,000
22 × 52 × 11 × 132 = 185,900
22 × 5 × 7 × 113 = 186,340
25 × 5 × 7 × 132 = 189,280
26 × 52 × 112 = 193,600
53 × 112 × 13 = 196,625
23 × 52 × 7 × 11 × 13 = 200,200
27 × 112 × 13 = 201,344
2 × 5 × 112 × 132 = 204,490
27 × 53 × 13 = 208,000
24 × 7 × 11 × 132 = 208,208
2 × 53 × 7 × 112 = 211,750
25 × 5 × 113 = 212,960
22 × 5 × 7 × 112 × 13 = 220,220
113 × 132 = 224,939
26 × 52 × 11 × 13 = 228,800
53 × 11 × 132 = 232,375
52 × 7 × 113 = 232,925
23 × 52 × 7 × 132 = 236,600
27 × 11 × 132 = 237,952
24 × 53 × 112 = 242,000
2 × 7 × 113 × 13 = 242,242
27 × 52 × 7 × 11 = 246,400
2 × 53 × 7 × 11 × 13 = 250,250
25 × 5 × 112 × 13 = 251,680
22 × 5 × 7 × 11 × 132 = 260,260
23 × 52 × 113 = 266,200
26 × 52 × 132 = 270,400
26 × 5 × 7 × 112 = 271,040
52 × 7 × 112 × 13 = 275,275
24 × 113 × 13 = 276,848
24 × 53 × 11 × 13 = 286,000
2 × 7 × 112 × 132 = 286,286
27 × 52 × 7 × 13 = 291,200
2 × 53 × 7 × 132 = 295,750
25 × 5 × 11 × 132 = 297,440
25 × 7 × 113 = 298,144
25 × 53 × 7 × 11 = 308,000
23 × 52 × 112 × 13 = 314,600
26 × 5 × 7 × 11 × 13 = 320,320
52 × 7 × 11 × 132 = 325,325
24 × 112 × 132 = 327,184
2 × 53 × 113 = 332,750
24 × 53 × 132 = 338,000
24 × 52 × 7 × 112 = 338,800
22 × 5 × 113 × 13 = 346,060
25 × 7 × 112 × 13 = 352,352
25 × 53 × 7 × 13 = 364,000
23 × 52 × 11 × 132 = 371,800
23 × 5 × 7 × 113 = 372,680
26 × 5 × 7 × 132 = 378,560
27 × 52 × 112 = 387,200
2 × 53 × 112 × 13 = 393,250
24 × 52 × 7 × 11 × 13 = 400,400
22 × 5 × 112 × 132 = 408,980
25 × 7 × 11 × 132 = 416,416
22 × 53 × 7 × 112 = 423,500
26 × 5 × 113 = 425,920
52 × 113 × 13 = 432,575
23 × 5 × 7 × 112 × 13 = 440,440
2 × 113 × 132 = 449,878
27 × 52 × 11 × 13 = 457,600
2 × 53 × 11 × 132 = 464,750
2 × 52 × 7 × 113 = 465,850
24 × 52 × 7 × 132 = 473,200
25 × 53 × 112 = 484,000
22 × 7 × 113 × 13 = 484,484
22 × 53 × 7 × 11 × 13 = 500,500
26 × 5 × 112 × 13 = 503,360
52 × 112 × 132 = 511,225
23 × 5 × 7 × 11 × 132 = 520,520
24 × 52 × 113 = 532,400
27 × 52 × 132 = 540,800
27 × 5 × 7 × 112 = 542,080
2 × 52 × 7 × 112 × 13 = 550,550
25 × 113 × 13 = 553,696
25 × 53 × 11 × 13 = 572,000
22 × 7 × 112 × 132 = 572,572
22 × 53 × 7 × 132 = 591,500
26 × 5 × 11 × 132 = 594,880
26 × 7 × 113 = 596,288
5 × 7 × 113 × 13 = 605,605
26 × 53 × 7 × 11 = 616,000
24 × 52 × 112 × 13 = 629,200
27 × 5 × 7 × 11 × 13 = 640,640
2 × 52 × 7 × 11 × 132 = 650,650
25 × 112 × 132 = 654,368
22 × 53 × 113 = 665,500
25 × 53 × 132 = 676,000
25 × 52 × 7 × 112 = 677,600
23 × 5 × 113 × 13 = 692,120
26 × 7 × 112 × 13 = 704,704
5 × 7 × 112 × 132 = 715,715
26 × 53 × 7 × 13 = 728,000
24 × 52 × 11 × 132 = 743,600
24 × 5 × 7 × 113 = 745,360
27 × 5 × 7 × 132 = 757,120
22 × 53 × 112 × 13 = 786,500
25 × 52 × 7 × 11 × 13 = 800,800
23 × 5 × 112 × 132 = 817,960
26 × 7 × 11 × 132 = 832,832
23 × 53 × 7 × 112 = 847,000
27 × 5 × 113 = 851,840
2 × 52 × 113 × 13 = 865,150
24 × 5 × 7 × 112 × 13 = 880,880
22 × 113 × 132 = 899,756
22 × 53 × 11 × 132 = 929,500
22 × 52 × 7 × 113 = 931,700
25 × 52 × 7 × 132 = 946,400
26 × 53 × 112 = 968,000
23 × 7 × 113 × 13 = 968,968
23 × 53 × 7 × 11 × 13 = 1,001,000
27 × 5 × 112 × 13 = 1,006,720
2 × 52 × 112 × 132 = 1,022,450
24 × 5 × 7 × 11 × 132 = 1,041,040
25 × 52 × 113 = 1,064,800
22 × 52 × 7 × 112 × 13 = 1,101,100
26 × 113 × 13 = 1,107,392
5 × 113 × 132 = 1,124,695
26 × 53 × 11 × 13 = 1,144,000
23 × 7 × 112 × 132 = 1,145,144
53 × 7 × 113 = 1,164,625
23 × 53 × 7 × 132 = 1,183,000
27 × 5 × 11 × 132 = 1,189,760
27 × 7 × 113 = 1,192,576
2 × 5 × 7 × 113 × 13 = 1,211,210
27 × 53 × 7 × 11 = 1,232,000
25 × 52 × 112 × 13 = 1,258,400
22 × 52 × 7 × 11 × 132 = 1,301,300
26 × 112 × 132 = 1,308,736
23 × 53 × 113 = 1,331,000
26 × 53 × 132 = 1,352,000
26 × 52 × 7 × 112 = 1,355,200
53 × 7 × 112 × 13 = 1,376,375
24 × 5 × 113 × 13 = 1,384,240
27 × 7 × 112 × 13 = 1,409,408
2 × 5 × 7 × 112 × 132 = 1,431,430
27 × 53 × 7 × 13 = 1,456,000
25 × 52 × 11 × 132 = 1,487,200
25 × 5 × 7 × 113 = 1,490,720
23 × 53 × 112 × 13 = 1,573,000
7 × 113 × 132 = 1,574,573
26 × 52 × 7 × 11 × 13 = 1,601,600
53 × 7 × 11 × 132 = 1,626,625
24 × 5 × 112 × 132 = 1,635,920
27 × 7 × 11 × 132 = 1,665,664
24 × 53 × 7 × 112 = 1,694,000
22 × 52 × 113 × 13 = 1,730,300
25 × 5 × 7 × 112 × 13 = 1,761,760
23 × 113 × 132 = 1,799,512
23 × 53 × 11 × 132 = 1,859,000
23 × 52 × 7 × 113 = 1,863,400
26 × 52 × 7 × 132 = 1,892,800
27 × 53 × 112 = 1,936,000
24 × 7 × 113 × 13 = 1,937,936
24 × 53 × 7 × 11 × 13 = 2,002,000
22 × 52 × 112 × 132 = 2,044,900
25 × 5 × 7 × 11 × 132 = 2,082,080
26 × 52 × 113 = 2,129,600
53 × 113 × 13 = 2,162,875
23 × 52 × 7 × 112 × 13 = 2,202,200
27 × 113 × 13 = 2,214,784
2 × 5 × 113 × 132 = 2,249,390
27 × 53 × 11 × 13 = 2,288,000
24 × 7 × 112 × 132 = 2,290,288
2 × 53 × 7 × 113 = 2,329,250
24 × 53 × 7 × 132 = 2,366,000
22 × 5 × 7 × 113 × 13 = 2,422,420
26 × 52 × 112 × 13 = 2,516,800
53 × 112 × 132 = 2,556,125
23 × 52 × 7 × 11 × 132 = 2,602,600
27 × 112 × 132 = 2,617,472
24 × 53 × 113 = 2,662,000
27 × 53 × 132 = 2,704,000
27 × 52 × 7 × 112 = 2,710,400
2 × 53 × 7 × 112 × 13 = 2,752,750
25 × 5 × 113 × 13 = 2,768,480
22 × 5 × 7 × 112 × 132 = 2,862,860
26 × 52 × 11 × 132 = 2,974,400
26 × 5 × 7 × 113 = 2,981,440
52 × 7 × 113 × 13 = 3,028,025
24 × 53 × 112 × 13 = 3,146,000
2 × 7 × 113 × 132 = 3,149,146
27 × 52 × 7 × 11 × 13 = 3,203,200
2 × 53 × 7 × 11 × 132 = 3,253,250
25 × 5 × 112 × 132 = 3,271,840
25 × 53 × 7 × 112 = 3,388,000
23 × 52 × 113 × 13 = 3,460,600
26 × 5 × 7 × 112 × 13 = 3,523,520
52 × 7 × 112 × 132 = 3,578,575
24 × 113 × 132 = 3,599,024
24 × 53 × 11 × 132 = 3,718,000
24 × 52 × 7 × 113 = 3,726,800
27 × 52 × 7 × 132 = 3,785,600
25 × 7 × 113 × 13 = 3,875,872
25 × 53 × 7 × 11 × 13 = 4,004,000
23 × 52 × 112 × 132 = 4,089,800
26 × 5 × 7 × 11 × 132 = 4,164,160
27 × 52 × 113 = 4,259,200
2 × 53 × 113 × 13 = 4,325,750
24 × 52 × 7 × 112 × 13 = 4,404,400
22 × 5 × 113 × 132 = 4,498,780
25 × 7 × 112 × 132 = 4,580,576
22 × 53 × 7 × 113 = 4,658,500
25 × 53 × 7 × 132 = 4,732,000
23 × 5 × 7 × 113 × 13 = 4,844,840
27 × 52 × 112 × 13 = 5,033,600
2 × 53 × 112 × 132 = 5,112,250
24 × 52 × 7 × 11 × 132 = 5,205,200
25 × 53 × 113 = 5,324,000
22 × 53 × 7 × 112 × 13 = 5,505,500
26 × 5 × 113 × 13 = 5,536,960
52 × 113 × 132 = 5,623,475
23 × 5 × 7 × 112 × 132 = 5,725,720
27 × 52 × 11 × 132 = 5,948,800
27 × 5 × 7 × 113 = 5,962,880
2 × 52 × 7 × 113 × 13 = 6,056,050
25 × 53 × 112 × 13 = 6,292,000
22 × 7 × 113 × 132 = 6,298,292
22 × 53 × 7 × 11 × 132 = 6,506,500
26 × 5 × 112 × 132 = 6,543,680
26 × 53 × 7 × 112 = 6,776,000
24 × 52 × 113 × 13 = 6,921,200
27 × 5 × 7 × 112 × 13 = 7,047,040
2 × 52 × 7 × 112 × 132 = 7,157,150
25 × 113 × 132 = 7,198,048
25 × 53 × 11 × 132 = 7,436,000
25 × 52 × 7 × 113 = 7,453,600
26 × 7 × 113 × 13 = 7,751,744
5 × 7 × 113 × 132 = 7,872,865
26 × 53 × 7 × 11 × 13 = 8,008,000
24 × 52 × 112 × 132 = 8,179,600
27 × 5 × 7 × 11 × 132 = 8,328,320
22 × 53 × 113 × 13 = 8,651,500
25 × 52 × 7 × 112 × 13 = 8,808,800
23 × 5 × 113 × 132 = 8,997,560
26 × 7 × 112 × 132 = 9,161,152
23 × 53 × 7 × 113 = 9,317,000
26 × 53 × 7 × 132 = 9,464,000
24 × 5 × 7 × 113 × 13 = 9,689,680
22 × 53 × 112 × 132 = 10,224,500
25 × 52 × 7 × 11 × 132 = 10,410,400
26 × 53 × 113 = 10,648,000
23 × 53 × 7 × 112 × 13 = 11,011,000
27 × 5 × 113 × 13 = 11,073,920
2 × 52 × 113 × 132 = 11,246,950
24 × 5 × 7 × 112 × 132 = 11,451,440
22 × 52 × 7 × 113 × 13 = 12,112,100
26 × 53 × 112 × 13 = 12,584,000
23 × 7 × 113 × 132 = 12,596,584
23 × 53 × 7 × 11 × 132 = 13,013,000
27 × 5 × 112 × 132 = 13,087,360
27 × 53 × 7 × 112 = 13,552,000
25 × 52 × 113 × 13 = 13,842,400
22 × 52 × 7 × 112 × 132 = 14,314,300
26 × 113 × 132 = 14,396,096
26 × 53 × 11 × 132 = 14,872,000
26 × 52 × 7 × 113 = 14,907,200
53 × 7 × 113 × 13 = 15,140,125
27 × 7 × 113 × 13 = 15,503,488
2 × 5 × 7 × 113 × 132 = 15,745,730
27 × 53 × 7 × 11 × 13 = 16,016,000
25 × 52 × 112 × 132 = 16,359,200
23 × 53 × 113 × 13 = 17,303,000
26 × 52 × 7 × 112 × 13 = 17,617,600
53 × 7 × 112 × 132 = 17,892,875
24 × 5 × 113 × 132 = 17,995,120
27 × 7 × 112 × 132 = 18,322,304
24 × 53 × 7 × 113 = 18,634,000
27 × 53 × 7 × 132 = 18,928,000
25 × 5 × 7 × 113 × 13 = 19,379,360
23 × 53 × 112 × 132 = 20,449,000
26 × 52 × 7 × 11 × 132 = 20,820,800
27 × 53 × 113 = 21,296,000
24 × 53 × 7 × 112 × 13 = 22,022,000
22 × 52 × 113 × 132 = 22,493,900
25 × 5 × 7 × 112 × 132 = 22,902,880
23 × 52 × 7 × 113 × 13 = 24,224,200
27 × 53 × 112 × 13 = 25,168,000
24 × 7 × 113 × 132 = 25,193,168
24 × 53 × 7 × 11 × 132 = 26,026,000
26 × 52 × 113 × 13 = 27,684,800
53 × 113 × 132 = 28,117,375
23 × 52 × 7 × 112 × 132 = 28,628,600
27 × 113 × 132 = 28,792,192
27 × 53 × 11 × 132 = 29,744,000
27 × 52 × 7 × 113 = 29,814,400
2 × 53 × 7 × 113 × 13 = 30,280,250
22 × 5 × 7 × 113 × 132 = 31,491,460
26 × 52 × 112 × 132 = 32,718,400
24 × 53 × 113 × 13 = 34,606,000
27 × 52 × 7 × 112 × 13 = 35,235,200
2 × 53 × 7 × 112 × 132 = 35,785,750
25 × 5 × 113 × 132 = 35,990,240
25 × 53 × 7 × 113 = 37,268,000
26 × 5 × 7 × 113 × 13 = 38,758,720
52 × 7 × 113 × 132 = 39,364,325
24 × 53 × 112 × 132 = 40,898,000
27 × 52 × 7 × 11 × 132 = 41,641,600
25 × 53 × 7 × 112 × 13 = 44,044,000
23 × 52 × 113 × 132 = 44,987,800
26 × 5 × 7 × 112 × 132 = 45,805,760
24 × 52 × 7 × 113 × 13 = 48,448,400
25 × 7 × 113 × 132 = 50,386,336
25 × 53 × 7 × 11 × 132 = 52,052,000
27 × 52 × 113 × 13 = 55,369,600
2 × 53 × 113 × 132 = 56,234,750
24 × 52 × 7 × 112 × 132 = 57,257,200
22 × 53 × 7 × 113 × 13 = 60,560,500
23 × 5 × 7 × 113 × 132 = 62,982,920
27 × 52 × 112 × 132 = 65,436,800
25 × 53 × 113 × 13 = 69,212,000
22 × 53 × 7 × 112 × 132 = 71,571,500
26 × 5 × 113 × 132 = 71,980,480
26 × 53 × 7 × 113 = 74,536,000
27 × 5 × 7 × 113 × 13 = 77,517,440
2 × 52 × 7 × 113 × 132 = 78,728,650
25 × 53 × 112 × 132 = 81,796,000
26 × 53 × 7 × 112 × 13 = 88,088,000
24 × 52 × 113 × 132 = 89,975,600
27 × 5 × 7 × 112 × 132 = 91,611,520
25 × 52 × 7 × 113 × 13 = 96,896,800
26 × 7 × 113 × 132 = 100,772,672
26 × 53 × 7 × 11 × 132 = 104,104,000
22 × 53 × 113 × 132 = 112,469,500
25 × 52 × 7 × 112 × 132 = 114,514,400
23 × 53 × 7 × 113 × 13 = 121,121,000
24 × 5 × 7 × 113 × 132 = 125,965,840
26 × 53 × 113 × 13 = 138,424,000
23 × 53 × 7 × 112 × 132 = 143,143,000
27 × 5 × 113 × 132 = 143,960,960
27 × 53 × 7 × 113 = 149,072,000
22 × 52 × 7 × 113 × 132 = 157,457,300
26 × 53 × 112 × 132 = 163,592,000
27 × 53 × 7 × 112 × 13 = 176,176,000
25 × 52 × 113 × 132 = 179,951,200
26 × 52 × 7 × 113 × 13 = 193,793,600
53 × 7 × 113 × 132 = 196,821,625
27 × 7 × 113 × 132 = 201,545,344
27 × 53 × 7 × 11 × 132 = 208,208,000
23 × 53 × 113 × 132 = 224,939,000
26 × 52 × 7 × 112 × 132 = 229,028,800
24 × 53 × 7 × 113 × 13 = 242,242,000
25 × 5 × 7 × 113 × 132 = 251,931,680
27 × 53 × 113 × 13 = 276,848,000
24 × 53 × 7 × 112 × 132 = 286,286,000
23 × 52 × 7 × 113 × 132 = 314,914,600
27 × 53 × 112 × 132 = 327,184,000
26 × 52 × 113 × 132 = 359,902,400
27 × 52 × 7 × 113 × 13 = 387,587,200
2 × 53 × 7 × 113 × 132 = 393,643,250
24 × 53 × 113 × 132 = 449,878,000
27 × 52 × 7 × 112 × 132 = 458,057,600
25 × 53 × 7 × 113 × 13 = 484,484,000
26 × 5 × 7 × 113 × 132 = 503,863,360
25 × 53 × 7 × 112 × 132 = 572,572,000
24 × 52 × 7 × 113 × 132 = 629,829,200
27 × 52 × 113 × 132 = 719,804,800
22 × 53 × 7 × 113 × 132 = 787,286,500
25 × 53 × 113 × 132 = 899,756,000
26 × 53 × 7 × 113 × 13 = 968,968,000
27 × 5 × 7 × 113 × 132 = 1,007,726,720
26 × 53 × 7 × 112 × 132 = 1,145,144,000
25 × 52 × 7 × 113 × 132 = 1,259,658,400
23 × 53 × 7 × 113 × 132 = 1,574,573,000
26 × 53 × 113 × 132 = 1,799,512,000
27 × 53 × 7 × 113 × 13 = 1,937,936,000
27 × 53 × 7 × 112 × 132 = 2,290,288,000
26 × 52 × 7 × 113 × 132 = 2,519,316,800
24 × 53 × 7 × 113 × 132 = 3,149,146,000
27 × 53 × 113 × 132 = 3,599,024,000
27 × 52 × 7 × 113 × 132 = 5,038,633,600
25 × 53 × 7 × 113 × 132 = 6,298,292,000
26 × 53 × 7 × 113 × 132 = 12,596,584,000
27 × 53 × 7 × 113 × 132 = 25,193,168,000

The final answer:
(scroll down)

25,193,168,000 has 768 factors (divisors):
1; 2; 4; 5; 7; 8; 10; 11; 13; 14; 16; 20; 22; 25; 26; 28; 32; 35; 40; 44; 50; 52; 55; 56; 64; 65; 70; 77; 80; 88; 91; 100; 104; 110; 112; 121; 125; 128; 130; 140; 143; 154; 160; 169; 175; 176; 182; 200; 208; 220; 224; 242; 250; 260; 275; 280; 286; 308; 320; 325; 338; 350; 352; 364; 385; 400; 416; 440; 448; 455; 484; 500; 520; 550; 560; 572; 605; 616; 640; 650; 676; 700; 704; 715; 728; 770; 800; 832; 845; 847; 875; 880; 896; 910; 968; 1,000; 1,001; 1,040; 1,100; 1,120; 1,144; 1,183; 1,210; 1,232; 1,300; 1,331; 1,352; 1,375; 1,400; 1,408; 1,430; 1,456; 1,540; 1,573; 1,600; 1,625; 1,664; 1,690; 1,694; 1,750; 1,760; 1,820; 1,859; 1,925; 1,936; 2,000; 2,002; 2,080; 2,200; 2,240; 2,275; 2,288; 2,366; 2,420; 2,464; 2,600; 2,662; 2,704; 2,750; 2,800; 2,860; 2,912; 3,025; 3,080; 3,146; 3,200; 3,250; 3,380; 3,388; 3,500; 3,520; 3,575; 3,640; 3,718; 3,850; 3,872; 4,000; 4,004; 4,160; 4,225; 4,235; 4,400; 4,480; 4,550; 4,576; 4,732; 4,840; 4,928; 5,005; 5,200; 5,324; 5,408; 5,500; 5,600; 5,720; 5,824; 5,915; 6,050; 6,160; 6,292; 6,500; 6,655; 6,760; 6,776; 7,000; 7,040; 7,150; 7,280; 7,436; 7,700; 7,744; 7,865; 8,000; 8,008; 8,320; 8,450; 8,470; 8,800; 9,100; 9,152; 9,295; 9,317; 9,464; 9,625; 9,680; 9,856; 10,010; 10,400; 10,648; 10,816; 11,000; 11,011; 11,200; 11,375; 11,440; 11,648; 11,830; 12,100; 12,320; 12,584; 13,000; 13,013; 13,310; 13,520; 13,552; 14,000; 14,300; 14,560; 14,872; 15,125; 15,400; 15,488; 15,730; 16,000; 16,016; 16,900; 16,940; 17,303; 17,600; 17,875; 18,200; 18,304; 18,590; 18,634; 18,928; 19,250; 19,360; 20,020; 20,449; 20,800; 21,125; 21,175; 21,296; 21,632; 22,000; 22,022; 22,400; 22,750; 22,880; 23,660; 24,200; 24,640; 25,025; 25,168; 26,000; 26,026; 26,620; 27,040; 27,104; 28,000; 28,600; 29,120; 29,575; 29,744; 30,250; 30,800; 31,460; 32,032; 33,275; 33,800; 33,880; 34,606; 35,200; 35,750; 36,400; 37,180; 37,268; 37,856; 38,500; 38,720; 39,325; 40,040; 40,898; 41,600; 42,250; 42,350; 42,592; 44,000; 44,044; 45,500; 45,760; 46,475; 46,585; 47,320; 48,400; 49,280; 50,050; 50,336; 52,000; 52,052; 53,240; 54,080; 54,208; 55,055; 56,000; 57,200; 58,240; 59,150; 59,488; 60,500; 61,600; 62,920; 64,064; 65,065; 66,550; 67,600; 67,760; 69,212; 71,500; 72,800; 74,360; 74,536; 75,712; 77,000; 77,440; 78,650; 80,080; 81,796; 84,500; 84,700; 85,184; 86,515; 88,000; 88,088; 91,000; 91,520; 92,950; 93,170; 94,640; 96,800; 100,100; 100,672; 102,245; 104,000; 104,104; 105,875; 106,480; 108,160; 108,416; 110,110; 112,000; 114,400; 118,300; 118,976; 121,000; 121,121; 123,200; 125,125; 125,840; 128,128; 130,130; 133,100; 135,200; 135,520; 138,424; 143,000; 143,143; 145,600; 147,875; 148,720; 149,072; 151,424; 154,000; 157,300; 160,160; 163,592; 166,375; 169,000; 169,400; 170,368; 173,030; 176,000; 176,176; 182,000; 185,900; 186,340; 189,280; 193,600; 196,625; 200,200; 201,344; 204,490; 208,000; 208,208; 211,750; 212,960; 220,220; 224,939; 228,800; 232,375; 232,925; 236,600; 237,952; 242,000; 242,242; 246,400; 250,250; 251,680; 260,260; 266,200; 270,400; 271,040; 275,275; 276,848; 286,000; 286,286; 291,200; 295,750; 297,440; 298,144; 308,000; 314,600; 320,320; 325,325; 327,184; 332,750; 338,000; 338,800; 346,060; 352,352; 364,000; 371,800; 372,680; 378,560; 387,200; 393,250; 400,400; 408,980; 416,416; 423,500; 425,920; 432,575; 440,440; 449,878; 457,600; 464,750; 465,850; 473,200; 484,000; 484,484; 500,500; 503,360; 511,225; 520,520; 532,400; 540,800; 542,080; 550,550; 553,696; 572,000; 572,572; 591,500; 594,880; 596,288; 605,605; 616,000; 629,200; 640,640; 650,650; 654,368; 665,500; 676,000; 677,600; 692,120; 704,704; 715,715; 728,000; 743,600; 745,360; 757,120; 786,500; 800,800; 817,960; 832,832; 847,000; 851,840; 865,150; 880,880; 899,756; 929,500; 931,700; 946,400; 968,000; 968,968; 1,001,000; 1,006,720; 1,022,450; 1,041,040; 1,064,800; 1,101,100; 1,107,392; 1,124,695; 1,144,000; 1,145,144; 1,164,625; 1,183,000; 1,189,760; 1,192,576; 1,211,210; 1,232,000; 1,258,400; 1,301,300; 1,308,736; 1,331,000; 1,352,000; 1,355,200; 1,376,375; 1,384,240; 1,409,408; 1,431,430; 1,456,000; 1,487,200; 1,490,720; 1,573,000; 1,574,573; 1,601,600; 1,626,625; 1,635,920; 1,665,664; 1,694,000; 1,730,300; 1,761,760; 1,799,512; 1,859,000; 1,863,400; 1,892,800; 1,936,000; 1,937,936; 2,002,000; 2,044,900; 2,082,080; 2,129,600; 2,162,875; 2,202,200; 2,214,784; 2,249,390; 2,288,000; 2,290,288; 2,329,250; 2,366,000; 2,422,420; 2,516,800; 2,556,125; 2,602,600; 2,617,472; 2,662,000; 2,704,000; 2,710,400; 2,752,750; 2,768,480; 2,862,860; 2,974,400; 2,981,440; 3,028,025; 3,146,000; 3,149,146; 3,203,200; 3,253,250; 3,271,840; 3,388,000; 3,460,600; 3,523,520; 3,578,575; 3,599,024; 3,718,000; 3,726,800; 3,785,600; 3,875,872; 4,004,000; 4,089,800; 4,164,160; 4,259,200; 4,325,750; 4,404,400; 4,498,780; 4,580,576; 4,658,500; 4,732,000; 4,844,840; 5,033,600; 5,112,250; 5,205,200; 5,324,000; 5,505,500; 5,536,960; 5,623,475; 5,725,720; 5,948,800; 5,962,880; 6,056,050; 6,292,000; 6,298,292; 6,506,500; 6,543,680; 6,776,000; 6,921,200; 7,047,040; 7,157,150; 7,198,048; 7,436,000; 7,453,600; 7,751,744; 7,872,865; 8,008,000; 8,179,600; 8,328,320; 8,651,500; 8,808,800; 8,997,560; 9,161,152; 9,317,000; 9,464,000; 9,689,680; 10,224,500; 10,410,400; 10,648,000; 11,011,000; 11,073,920; 11,246,950; 11,451,440; 12,112,100; 12,584,000; 12,596,584; 13,013,000; 13,087,360; 13,552,000; 13,842,400; 14,314,300; 14,396,096; 14,872,000; 14,907,200; 15,140,125; 15,503,488; 15,745,730; 16,016,000; 16,359,200; 17,303,000; 17,617,600; 17,892,875; 17,995,120; 18,322,304; 18,634,000; 18,928,000; 19,379,360; 20,449,000; 20,820,800; 21,296,000; 22,022,000; 22,493,900; 22,902,880; 24,224,200; 25,168,000; 25,193,168; 26,026,000; 27,684,800; 28,117,375; 28,628,600; 28,792,192; 29,744,000; 29,814,400; 30,280,250; 31,491,460; 32,718,400; 34,606,000; 35,235,200; 35,785,750; 35,990,240; 37,268,000; 38,758,720; 39,364,325; 40,898,000; 41,641,600; 44,044,000; 44,987,800; 45,805,760; 48,448,400; 50,386,336; 52,052,000; 55,369,600; 56,234,750; 57,257,200; 60,560,500; 62,982,920; 65,436,800; 69,212,000; 71,571,500; 71,980,480; 74,536,000; 77,517,440; 78,728,650; 81,796,000; 88,088,000; 89,975,600; 91,611,520; 96,896,800; 100,772,672; 104,104,000; 112,469,500; 114,514,400; 121,121,000; 125,965,840; 138,424,000; 143,143,000; 143,960,960; 149,072,000; 157,457,300; 163,592,000; 176,176,000; 179,951,200; 193,793,600; 196,821,625; 201,545,344; 208,208,000; 224,939,000; 229,028,800; 242,242,000; 251,931,680; 276,848,000; 286,286,000; 314,914,600; 327,184,000; 359,902,400; 387,587,200; 393,643,250; 449,878,000; 458,057,600; 484,484,000; 503,863,360; 572,572,000; 629,829,200; 719,804,800; 787,286,500; 899,756,000; 968,968,000; 1,007,726,720; 1,145,144,000; 1,259,658,400; 1,574,573,000; 1,799,512,000; 1,937,936,000; 2,290,288,000; 2,519,316,800; 3,149,146,000; 3,599,024,000; 5,038,633,600; 6,298,292,000; 12,596,584,000 and 25,193,168,000
out of which 5 prime factors: 2; 5; 7; 11 and 13
25,193,168,000 and 1 are sometimes called improper factors, the others are called proper factors (proper divisors).

A quick way to find the factors (the divisors) of a number is to break it down into prime factors.


Then multiply the prime factors and their exponents, if any, in all their different combinations.


Calculate all the divisors (factors) of the given numbers

How to calculate (find) all the factors (divisors) of a number:

Break down the number into prime factors. Then multiply its prime factors in all their unique combinations, that give different results.

To calculate the common factors of two numbers:

The common factors (divisors) of two numbers are all the factors of the greatest common factor, gcf.

Calculate the greatest (highest) common factor (divisor) of the two numbers, gcf (hcf, gcd).

Break down the GCF into prime factors. Then multiply its prime factors in all their unique combinations, that give different results.

The latest 10 sets of calculated factors (divisors): of one number or the common factors of two numbers

What are all the proper, improper and prime factors (all the divisors) of the number 25,193,168,000? How to calculate them? Apr 20 13:14 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 259,952,470? How to calculate them? Apr 20 13:14 UTC (GMT)
What are all the common factors (all the divisors and the prime factors) of the numbers 1,637 and 0? How to calculate them? Apr 20 13:14 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 44,880? How to calculate them? Apr 20 13:14 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 1,495? How to calculate them? Apr 20 13:14 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 232,599? How to calculate them? Apr 20 13:14 UTC (GMT)
What are all the common factors (all the divisors and the prime factors) of the numbers 48 and 38? How to calculate them? Apr 20 13:14 UTC (GMT)
What are all the common factors (all the divisors and the prime factors) of the numbers 1,848 and 2,040? How to calculate them? Apr 20 13:14 UTC (GMT)
What are all the common factors (all the divisors and the prime factors) of the numbers 45 and 24? How to calculate them? Apr 20 13:14 UTC (GMT)
What are all the common factors (all the divisors and the prime factors) of the numbers 122,805,144 and 0? How to calculate them? Apr 20 13:14 UTC (GMT)
The list of all the calculated factors (divisors) of one or two numbers

Factors (divisors), common factors (common divisors), the greatest common factor, GCF (also called the greatest common divisor, GCD, or the highest common factor, HCF)

  • If the number "t" is a factor (divisor) of the number "a" then in the prime factorization of "t" we will only encounter prime factors that also occur in the prime factorization of "a".
  • If there are exponents involved, the maximum value of an exponent for any base of a power that is found in the prime factorization of "t" (powers, or multiplicities) is at most equal to the exponent of the same base that is involved in the prime factorization of "a".
  • Hint: 23 = 2 × 2 × 2 = 8. 2 is called the base and 3 is the exponent. 23 is the power and 8 is the value of the power. We sometimes say that the number 2 is raised to the power of 3.
  • For example, 12 is a factor (divisor) of 120 - the remainder is zero when dividing 120 by 12.
  • Let's look at the prime factorization of both numbers and notice the bases and the exponents that occur in the prime factorization of both numbers:
  • 12 = 2 × 2 × 3 = 22 × 3
  • 120 = 2 × 2 × 2 × 3 × 5 = 23 × 3 × 5
  • 120 contains all the prime factors of 12, and all its bases' exponents are higher than those of 12.
  • If "t" is a common factor (divisor) of "a" and "b", then the prime factorization of "t" contains only the common prime factors involved in the prime factorizations of both "a" and "b".
  • If there are exponents involved, the maximum value of an exponent for any base of a power that is found in the prime factorization of "t" is at most equal to the minimum of the exponents of the same base that is involved in the prime factorization of both "a" and "b".
  • For example, 12 is the common factor of 48 and 360.
  • The remainder is zero when dividing either 48 or 360 by 12.
  • Here there are the prime factorizations of the three numbers, 12, 48 and 360:
  • 12 = 22 × 3
  • 48 = 24 × 3
  • 360 = 23 × 32 × 5
  • Please note that 48 and 360 have more factors (divisors): 2, 3, 4, 6, 8, 12, 24. Among them, 24 is the greatest common factor, GCF (or the greatest common divisor, GCD, or the highest common factor, HCF) of 48 and 360.
  • The greatest common factor, GCF, of two numbers, "a" and "b", is the product of all the common prime factors involved in the prime factorizations of both "a" and "b", taken by the lowest exponents.
  • Based on this rule it is calculated the greatest common factor, GCF, (or the greatest common divisor GCD, HCF) of several numbers, as shown in the example below...
  • GCF, GCD (1,260; 3,024; 5,544) = ?
  • 1,260 = 22 × 32
  • 3,024 = 24 × 32 × 7
  • 5,544 = 23 × 32 × 7 × 11
  • The common prime factors are:
  • 2 - its lowest exponent (multiplicity) is: min.(2; 3; 4) = 2
  • 3 - its lowest exponent (multiplicity) is: min.(2; 2; 2) = 2
  • GCF, GCD (1,260; 3,024; 5,544) = 22 × 32 = 252
  • Coprime numbers:
  • If two numbers "a" and "b" have no other common factors (divisors) than 1, gfc, gcd, hcf (a; b) = 1, then the numbers "a" and "b" are called coprime (or relatively prime).
  • Factors of the GCF
  • If "a" and "b" are not coprime, then every common factor (divisor) of "a" and "b" is a also a factor (divisor) of the greatest common factor, GCF (greatest common divisor, GCD, highest common factor, HCF) of "a" and "b".