Given the Number 163,785,600, Calculate (Find) All the Factors (All the Divisors) of the Number 163,785,600 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 163,785,600

1. Carry out the prime factorization of the number 163,785,600:

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


163,785,600 = 27 × 32 × 52 × 112 × 47
163,785,600 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 163,785,600

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
prime factor = 3
22 = 4
prime factor = 5
2 × 3 = 6
23 = 8
32 = 9
2 × 5 = 10
prime factor = 11
22 × 3 = 12
3 × 5 = 15
24 = 16
2 × 32 = 18
22 × 5 = 20
2 × 11 = 22
23 × 3 = 24
52 = 25
2 × 3 × 5 = 30
25 = 32
3 × 11 = 33
22 × 32 = 36
23 × 5 = 40
22 × 11 = 44
32 × 5 = 45
prime factor = 47
24 × 3 = 48
2 × 52 = 50
5 × 11 = 55
22 × 3 × 5 = 60
26 = 64
2 × 3 × 11 = 66
23 × 32 = 72
3 × 52 = 75
24 × 5 = 80
23 × 11 = 88
2 × 32 × 5 = 90
2 × 47 = 94
25 × 3 = 96
32 × 11 = 99
22 × 52 = 100
2 × 5 × 11 = 110
23 × 3 × 5 = 120
112 = 121
27 = 128
22 × 3 × 11 = 132
3 × 47 = 141
24 × 32 = 144
2 × 3 × 52 = 150
25 × 5 = 160
3 × 5 × 11 = 165
24 × 11 = 176
22 × 32 × 5 = 180
22 × 47 = 188
26 × 3 = 192
2 × 32 × 11 = 198
23 × 52 = 200
22 × 5 × 11 = 220
32 × 52 = 225
5 × 47 = 235
24 × 3 × 5 = 240
2 × 112 = 242
23 × 3 × 11 = 264
52 × 11 = 275
2 × 3 × 47 = 282
25 × 32 = 288
22 × 3 × 52 = 300
26 × 5 = 320
2 × 3 × 5 × 11 = 330
25 × 11 = 352
23 × 32 × 5 = 360
3 × 112 = 363
23 × 47 = 376
27 × 3 = 384
22 × 32 × 11 = 396
24 × 52 = 400
32 × 47 = 423
23 × 5 × 11 = 440
2 × 32 × 52 = 450
2 × 5 × 47 = 470
25 × 3 × 5 = 480
22 × 112 = 484
32 × 5 × 11 = 495
11 × 47 = 517
24 × 3 × 11 = 528
2 × 52 × 11 = 550
22 × 3 × 47 = 564
26 × 32 = 576
23 × 3 × 52 = 600
5 × 112 = 605
27 × 5 = 640
22 × 3 × 5 × 11 = 660
26 × 11 = 704
3 × 5 × 47 = 705
24 × 32 × 5 = 720
2 × 3 × 112 = 726
24 × 47 = 752
23 × 32 × 11 = 792
25 × 52 = 800
3 × 52 × 11 = 825
2 × 32 × 47 = 846
24 × 5 × 11 = 880
22 × 32 × 52 = 900
22 × 5 × 47 = 940
26 × 3 × 5 = 960
23 × 112 = 968
2 × 32 × 5 × 11 = 990
2 × 11 × 47 = 1,034
25 × 3 × 11 = 1,056
32 × 112 = 1,089
22 × 52 × 11 = 1,100
23 × 3 × 47 = 1,128
27 × 32 = 1,152
52 × 47 = 1,175
24 × 3 × 52 = 1,200
2 × 5 × 112 = 1,210
23 × 3 × 5 × 11 = 1,320
27 × 11 = 1,408
2 × 3 × 5 × 47 = 1,410
25 × 32 × 5 = 1,440
22 × 3 × 112 = 1,452
25 × 47 = 1,504
3 × 11 × 47 = 1,551
24 × 32 × 11 = 1,584
26 × 52 = 1,600
2 × 3 × 52 × 11 = 1,650
22 × 32 × 47 = 1,692
25 × 5 × 11 = 1,760
23 × 32 × 52 = 1,800
3 × 5 × 112 = 1,815
23 × 5 × 47 = 1,880
27 × 3 × 5 = 1,920
24 × 112 = 1,936
22 × 32 × 5 × 11 = 1,980
22 × 11 × 47 = 2,068
26 × 3 × 11 = 2,112
32 × 5 × 47 = 2,115
2 × 32 × 112 = 2,178
23 × 52 × 11 = 2,200
24 × 3 × 47 = 2,256
2 × 52 × 47 = 2,350
25 × 3 × 52 = 2,400
22 × 5 × 112 = 2,420
32 × 52 × 11 = 2,475
5 × 11 × 47 = 2,585
24 × 3 × 5 × 11 = 2,640
22 × 3 × 5 × 47 = 2,820
26 × 32 × 5 = 2,880
23 × 3 × 112 = 2,904
26 × 47 = 3,008
52 × 112 = 3,025
2 × 3 × 11 × 47 = 3,102
25 × 32 × 11 = 3,168
27 × 52 = 3,200
22 × 3 × 52 × 11 = 3,300
23 × 32 × 47 = 3,384
26 × 5 × 11 = 3,520
3 × 52 × 47 = 3,525
24 × 32 × 52 = 3,600
2 × 3 × 5 × 112 = 3,630
24 × 5 × 47 = 3,760
25 × 112 = 3,872
23 × 32 × 5 × 11 = 3,960
23 × 11 × 47 = 4,136
27 × 3 × 11 = 4,224
2 × 32 × 5 × 47 = 4,230
22 × 32 × 112 = 4,356
24 × 52 × 11 = 4,400
25 × 3 × 47 = 4,512
32 × 11 × 47 = 4,653
22 × 52 × 47 = 4,700
26 × 3 × 52 = 4,800
23 × 5 × 112 = 4,840
2 × 32 × 52 × 11 = 4,950
2 × 5 × 11 × 47 = 5,170
25 × 3 × 5 × 11 = 5,280
32 × 5 × 112 = 5,445
23 × 3 × 5 × 47 = 5,640
112 × 47 = 5,687
27 × 32 × 5 = 5,760
24 × 3 × 112 = 5,808
27 × 47 = 6,016
2 × 52 × 112 = 6,050
22 × 3 × 11 × 47 = 6,204
26 × 32 × 11 = 6,336
23 × 3 × 52 × 11 = 6,600
24 × 32 × 47 = 6,768
27 × 5 × 11 = 7,040
2 × 3 × 52 × 47 = 7,050
25 × 32 × 52 = 7,200
22 × 3 × 5 × 112 = 7,260
25 × 5 × 47 = 7,520
26 × 112 = 7,744
3 × 5 × 11 × 47 = 7,755
24 × 32 × 5 × 11 = 7,920
24 × 11 × 47 = 8,272
22 × 32 × 5 × 47 = 8,460
23 × 32 × 112 = 8,712
25 × 52 × 11 = 8,800
26 × 3 × 47 = 9,024
3 × 52 × 112 = 9,075
2 × 32 × 11 × 47 = 9,306
23 × 52 × 47 = 9,400
27 × 3 × 52 = 9,600
24 × 5 × 112 = 9,680
22 × 32 × 52 × 11 = 9,900
22 × 5 × 11 × 47 = 10,340
26 × 3 × 5 × 11 = 10,560
32 × 52 × 47 = 10,575
2 × 32 × 5 × 112 = 10,890
24 × 3 × 5 × 47 = 11,280
2 × 112 × 47 = 11,374
25 × 3 × 112 = 11,616
22 × 52 × 112 = 12,100
23 × 3 × 11 × 47 = 12,408
27 × 32 × 11 = 12,672
This list continues below...

... This list continues from above
52 × 11 × 47 = 12,925
24 × 3 × 52 × 11 = 13,200
25 × 32 × 47 = 13,536
22 × 3 × 52 × 47 = 14,100
26 × 32 × 52 = 14,400
23 × 3 × 5 × 112 = 14,520
26 × 5 × 47 = 15,040
27 × 112 = 15,488
2 × 3 × 5 × 11 × 47 = 15,510
25 × 32 × 5 × 11 = 15,840
25 × 11 × 47 = 16,544
23 × 32 × 5 × 47 = 16,920
3 × 112 × 47 = 17,061
24 × 32 × 112 = 17,424
26 × 52 × 11 = 17,600
27 × 3 × 47 = 18,048
2 × 3 × 52 × 112 = 18,150
22 × 32 × 11 × 47 = 18,612
24 × 52 × 47 = 18,800
25 × 5 × 112 = 19,360
23 × 32 × 52 × 11 = 19,800
23 × 5 × 11 × 47 = 20,680
27 × 3 × 5 × 11 = 21,120
2 × 32 × 52 × 47 = 21,150
22 × 32 × 5 × 112 = 21,780
25 × 3 × 5 × 47 = 22,560
22 × 112 × 47 = 22,748
26 × 3 × 112 = 23,232
32 × 5 × 11 × 47 = 23,265
23 × 52 × 112 = 24,200
24 × 3 × 11 × 47 = 24,816
2 × 52 × 11 × 47 = 25,850
25 × 3 × 52 × 11 = 26,400
26 × 32 × 47 = 27,072
32 × 52 × 112 = 27,225
23 × 3 × 52 × 47 = 28,200
5 × 112 × 47 = 28,435
27 × 32 × 52 = 28,800
24 × 3 × 5 × 112 = 29,040
27 × 5 × 47 = 30,080
22 × 3 × 5 × 11 × 47 = 31,020
26 × 32 × 5 × 11 = 31,680
26 × 11 × 47 = 33,088
24 × 32 × 5 × 47 = 33,840
2 × 3 × 112 × 47 = 34,122
25 × 32 × 112 = 34,848
27 × 52 × 11 = 35,200
22 × 3 × 52 × 112 = 36,300
23 × 32 × 11 × 47 = 37,224
25 × 52 × 47 = 37,600
26 × 5 × 112 = 38,720
3 × 52 × 11 × 47 = 38,775
24 × 32 × 52 × 11 = 39,600
24 × 5 × 11 × 47 = 41,360
22 × 32 × 52 × 47 = 42,300
23 × 32 × 5 × 112 = 43,560
26 × 3 × 5 × 47 = 45,120
23 × 112 × 47 = 45,496
27 × 3 × 112 = 46,464
2 × 32 × 5 × 11 × 47 = 46,530
24 × 52 × 112 = 48,400
25 × 3 × 11 × 47 = 49,632
32 × 112 × 47 = 51,183
22 × 52 × 11 × 47 = 51,700
26 × 3 × 52 × 11 = 52,800
27 × 32 × 47 = 54,144
2 × 32 × 52 × 112 = 54,450
24 × 3 × 52 × 47 = 56,400
2 × 5 × 112 × 47 = 56,870
25 × 3 × 5 × 112 = 58,080
23 × 3 × 5 × 11 × 47 = 62,040
27 × 32 × 5 × 11 = 63,360
27 × 11 × 47 = 66,176
25 × 32 × 5 × 47 = 67,680
22 × 3 × 112 × 47 = 68,244
26 × 32 × 112 = 69,696
23 × 3 × 52 × 112 = 72,600
24 × 32 × 11 × 47 = 74,448
26 × 52 × 47 = 75,200
27 × 5 × 112 = 77,440
2 × 3 × 52 × 11 × 47 = 77,550
25 × 32 × 52 × 11 = 79,200
25 × 5 × 11 × 47 = 82,720
23 × 32 × 52 × 47 = 84,600
3 × 5 × 112 × 47 = 85,305
24 × 32 × 5 × 112 = 87,120
27 × 3 × 5 × 47 = 90,240
24 × 112 × 47 = 90,992
22 × 32 × 5 × 11 × 47 = 93,060
25 × 52 × 112 = 96,800
26 × 3 × 11 × 47 = 99,264
2 × 32 × 112 × 47 = 102,366
23 × 52 × 11 × 47 = 103,400
27 × 3 × 52 × 11 = 105,600
22 × 32 × 52 × 112 = 108,900
25 × 3 × 52 × 47 = 112,800
22 × 5 × 112 × 47 = 113,740
26 × 3 × 5 × 112 = 116,160
32 × 52 × 11 × 47 = 116,325
24 × 3 × 5 × 11 × 47 = 124,080
26 × 32 × 5 × 47 = 135,360
23 × 3 × 112 × 47 = 136,488
27 × 32 × 112 = 139,392
52 × 112 × 47 = 142,175
24 × 3 × 52 × 112 = 145,200
25 × 32 × 11 × 47 = 148,896
27 × 52 × 47 = 150,400
22 × 3 × 52 × 11 × 47 = 155,100
26 × 32 × 52 × 11 = 158,400
26 × 5 × 11 × 47 = 165,440
24 × 32 × 52 × 47 = 169,200
2 × 3 × 5 × 112 × 47 = 170,610
25 × 32 × 5 × 112 = 174,240
25 × 112 × 47 = 181,984
23 × 32 × 5 × 11 × 47 = 186,120
26 × 52 × 112 = 193,600
27 × 3 × 11 × 47 = 198,528
22 × 32 × 112 × 47 = 204,732
24 × 52 × 11 × 47 = 206,800
23 × 32 × 52 × 112 = 217,800
26 × 3 × 52 × 47 = 225,600
23 × 5 × 112 × 47 = 227,480
27 × 3 × 5 × 112 = 232,320
2 × 32 × 52 × 11 × 47 = 232,650
25 × 3 × 5 × 11 × 47 = 248,160
32 × 5 × 112 × 47 = 255,915
27 × 32 × 5 × 47 = 270,720
24 × 3 × 112 × 47 = 272,976
2 × 52 × 112 × 47 = 284,350
25 × 3 × 52 × 112 = 290,400
26 × 32 × 11 × 47 = 297,792
23 × 3 × 52 × 11 × 47 = 310,200
27 × 32 × 52 × 11 = 316,800
27 × 5 × 11 × 47 = 330,880
25 × 32 × 52 × 47 = 338,400
22 × 3 × 5 × 112 × 47 = 341,220
26 × 32 × 5 × 112 = 348,480
26 × 112 × 47 = 363,968
24 × 32 × 5 × 11 × 47 = 372,240
27 × 52 × 112 = 387,200
23 × 32 × 112 × 47 = 409,464
25 × 52 × 11 × 47 = 413,600
3 × 52 × 112 × 47 = 426,525
24 × 32 × 52 × 112 = 435,600
27 × 3 × 52 × 47 = 451,200
24 × 5 × 112 × 47 = 454,960
22 × 32 × 52 × 11 × 47 = 465,300
26 × 3 × 5 × 11 × 47 = 496,320
2 × 32 × 5 × 112 × 47 = 511,830
25 × 3 × 112 × 47 = 545,952
22 × 52 × 112 × 47 = 568,700
26 × 3 × 52 × 112 = 580,800
27 × 32 × 11 × 47 = 595,584
24 × 3 × 52 × 11 × 47 = 620,400
26 × 32 × 52 × 47 = 676,800
23 × 3 × 5 × 112 × 47 = 682,440
27 × 32 × 5 × 112 = 696,960
27 × 112 × 47 = 727,936
25 × 32 × 5 × 11 × 47 = 744,480
24 × 32 × 112 × 47 = 818,928
26 × 52 × 11 × 47 = 827,200
2 × 3 × 52 × 112 × 47 = 853,050
25 × 32 × 52 × 112 = 871,200
25 × 5 × 112 × 47 = 909,920
23 × 32 × 52 × 11 × 47 = 930,600
27 × 3 × 5 × 11 × 47 = 992,640
22 × 32 × 5 × 112 × 47 = 1,023,660
26 × 3 × 112 × 47 = 1,091,904
23 × 52 × 112 × 47 = 1,137,400
27 × 3 × 52 × 112 = 1,161,600
25 × 3 × 52 × 11 × 47 = 1,240,800
32 × 52 × 112 × 47 = 1,279,575
27 × 32 × 52 × 47 = 1,353,600
24 × 3 × 5 × 112 × 47 = 1,364,880
26 × 32 × 5 × 11 × 47 = 1,488,960
25 × 32 × 112 × 47 = 1,637,856
27 × 52 × 11 × 47 = 1,654,400
22 × 3 × 52 × 112 × 47 = 1,706,100
26 × 32 × 52 × 112 = 1,742,400
26 × 5 × 112 × 47 = 1,819,840
24 × 32 × 52 × 11 × 47 = 1,861,200
23 × 32 × 5 × 112 × 47 = 2,047,320
27 × 3 × 112 × 47 = 2,183,808
24 × 52 × 112 × 47 = 2,274,800
26 × 3 × 52 × 11 × 47 = 2,481,600
2 × 32 × 52 × 112 × 47 = 2,559,150
25 × 3 × 5 × 112 × 47 = 2,729,760
27 × 32 × 5 × 11 × 47 = 2,977,920
26 × 32 × 112 × 47 = 3,275,712
23 × 3 × 52 × 112 × 47 = 3,412,200
27 × 32 × 52 × 112 = 3,484,800
27 × 5 × 112 × 47 = 3,639,680
25 × 32 × 52 × 11 × 47 = 3,722,400
24 × 32 × 5 × 112 × 47 = 4,094,640
25 × 52 × 112 × 47 = 4,549,600
27 × 3 × 52 × 11 × 47 = 4,963,200
22 × 32 × 52 × 112 × 47 = 5,118,300
26 × 3 × 5 × 112 × 47 = 5,459,520
27 × 32 × 112 × 47 = 6,551,424
24 × 3 × 52 × 112 × 47 = 6,824,400
26 × 32 × 52 × 11 × 47 = 7,444,800
25 × 32 × 5 × 112 × 47 = 8,189,280
26 × 52 × 112 × 47 = 9,099,200
23 × 32 × 52 × 112 × 47 = 10,236,600
27 × 3 × 5 × 112 × 47 = 10,919,040
25 × 3 × 52 × 112 × 47 = 13,648,800
27 × 32 × 52 × 11 × 47 = 14,889,600
26 × 32 × 5 × 112 × 47 = 16,378,560
27 × 52 × 112 × 47 = 18,198,400
24 × 32 × 52 × 112 × 47 = 20,473,200
26 × 3 × 52 × 112 × 47 = 27,297,600
27 × 32 × 5 × 112 × 47 = 32,757,120
25 × 32 × 52 × 112 × 47 = 40,946,400
27 × 3 × 52 × 112 × 47 = 54,595,200
26 × 32 × 52 × 112 × 47 = 81,892,800
27 × 32 × 52 × 112 × 47 = 163,785,600

The final answer:
(scroll down)

163,785,600 has 432 factors (divisors):
1; 2; 3; 4; 5; 6; 8; 9; 10; 11; 12; 15; 16; 18; 20; 22; 24; 25; 30; 32; 33; 36; 40; 44; 45; 47; 48; 50; 55; 60; 64; 66; 72; 75; 80; 88; 90; 94; 96; 99; 100; 110; 120; 121; 128; 132; 141; 144; 150; 160; 165; 176; 180; 188; 192; 198; 200; 220; 225; 235; 240; 242; 264; 275; 282; 288; 300; 320; 330; 352; 360; 363; 376; 384; 396; 400; 423; 440; 450; 470; 480; 484; 495; 517; 528; 550; 564; 576; 600; 605; 640; 660; 704; 705; 720; 726; 752; 792; 800; 825; 846; 880; 900; 940; 960; 968; 990; 1,034; 1,056; 1,089; 1,100; 1,128; 1,152; 1,175; 1,200; 1,210; 1,320; 1,408; 1,410; 1,440; 1,452; 1,504; 1,551; 1,584; 1,600; 1,650; 1,692; 1,760; 1,800; 1,815; 1,880; 1,920; 1,936; 1,980; 2,068; 2,112; 2,115; 2,178; 2,200; 2,256; 2,350; 2,400; 2,420; 2,475; 2,585; 2,640; 2,820; 2,880; 2,904; 3,008; 3,025; 3,102; 3,168; 3,200; 3,300; 3,384; 3,520; 3,525; 3,600; 3,630; 3,760; 3,872; 3,960; 4,136; 4,224; 4,230; 4,356; 4,400; 4,512; 4,653; 4,700; 4,800; 4,840; 4,950; 5,170; 5,280; 5,445; 5,640; 5,687; 5,760; 5,808; 6,016; 6,050; 6,204; 6,336; 6,600; 6,768; 7,040; 7,050; 7,200; 7,260; 7,520; 7,744; 7,755; 7,920; 8,272; 8,460; 8,712; 8,800; 9,024; 9,075; 9,306; 9,400; 9,600; 9,680; 9,900; 10,340; 10,560; 10,575; 10,890; 11,280; 11,374; 11,616; 12,100; 12,408; 12,672; 12,925; 13,200; 13,536; 14,100; 14,400; 14,520; 15,040; 15,488; 15,510; 15,840; 16,544; 16,920; 17,061; 17,424; 17,600; 18,048; 18,150; 18,612; 18,800; 19,360; 19,800; 20,680; 21,120; 21,150; 21,780; 22,560; 22,748; 23,232; 23,265; 24,200; 24,816; 25,850; 26,400; 27,072; 27,225; 28,200; 28,435; 28,800; 29,040; 30,080; 31,020; 31,680; 33,088; 33,840; 34,122; 34,848; 35,200; 36,300; 37,224; 37,600; 38,720; 38,775; 39,600; 41,360; 42,300; 43,560; 45,120; 45,496; 46,464; 46,530; 48,400; 49,632; 51,183; 51,700; 52,800; 54,144; 54,450; 56,400; 56,870; 58,080; 62,040; 63,360; 66,176; 67,680; 68,244; 69,696; 72,600; 74,448; 75,200; 77,440; 77,550; 79,200; 82,720; 84,600; 85,305; 87,120; 90,240; 90,992; 93,060; 96,800; 99,264; 102,366; 103,400; 105,600; 108,900; 112,800; 113,740; 116,160; 116,325; 124,080; 135,360; 136,488; 139,392; 142,175; 145,200; 148,896; 150,400; 155,100; 158,400; 165,440; 169,200; 170,610; 174,240; 181,984; 186,120; 193,600; 198,528; 204,732; 206,800; 217,800; 225,600; 227,480; 232,320; 232,650; 248,160; 255,915; 270,720; 272,976; 284,350; 290,400; 297,792; 310,200; 316,800; 330,880; 338,400; 341,220; 348,480; 363,968; 372,240; 387,200; 409,464; 413,600; 426,525; 435,600; 451,200; 454,960; 465,300; 496,320; 511,830; 545,952; 568,700; 580,800; 595,584; 620,400; 676,800; 682,440; 696,960; 727,936; 744,480; 818,928; 827,200; 853,050; 871,200; 909,920; 930,600; 992,640; 1,023,660; 1,091,904; 1,137,400; 1,161,600; 1,240,800; 1,279,575; 1,353,600; 1,364,880; 1,488,960; 1,637,856; 1,654,400; 1,706,100; 1,742,400; 1,819,840; 1,861,200; 2,047,320; 2,183,808; 2,274,800; 2,481,600; 2,559,150; 2,729,760; 2,977,920; 3,275,712; 3,412,200; 3,484,800; 3,639,680; 3,722,400; 4,094,640; 4,549,600; 4,963,200; 5,118,300; 5,459,520; 6,551,424; 6,824,400; 7,444,800; 8,189,280; 9,099,200; 10,236,600; 10,919,040; 13,648,800; 14,889,600; 16,378,560; 18,198,400; 20,473,200; 27,297,600; 32,757,120; 40,946,400; 54,595,200; 81,892,800 and 163,785,600
out of which 5 prime factors: 2; 3; 5; 11 and 47
163,785,600 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

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".