Given the Number 17,635,800, Calculate (Find) All the Factors (All the Divisors) of the Number 17,635,800 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 17,635,800

1. Carry out the prime factorization of the number 17,635,800:

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

17,635,800 = 23 × 3 × 52 × 7 × 13 × 17 × 19
17,635,800 is not a prime number but a composite one.

» Online calculator. Check whether a number is prime or not. The prime factorization of composite numbers

* 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 17,635,800

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
prime factor = 7
23 = 8
2 × 5 = 10
22 × 3 = 12
prime factor = 13
2 × 7 = 14
3 × 5 = 15
prime factor = 17
prime factor = 19
22 × 5 = 20
3 × 7 = 21
23 × 3 = 24
52 = 25
2 × 13 = 26
22 × 7 = 28
2 × 3 × 5 = 30
2 × 17 = 34
5 × 7 = 35
2 × 19 = 38
3 × 13 = 39
23 × 5 = 40
2 × 3 × 7 = 42
2 × 52 = 50
3 × 17 = 51
22 × 13 = 52
23 × 7 = 56
3 × 19 = 57
22 × 3 × 5 = 60
5 × 13 = 65
22 × 17 = 68
2 × 5 × 7 = 70
3 × 52 = 75
22 × 19 = 76
2 × 3 × 13 = 78
22 × 3 × 7 = 84
5 × 17 = 85
7 × 13 = 91
5 × 19 = 95
22 × 52 = 100
2 × 3 × 17 = 102
23 × 13 = 104
3 × 5 × 7 = 105
2 × 3 × 19 = 114
7 × 17 = 119
23 × 3 × 5 = 120
2 × 5 × 13 = 130
7 × 19 = 133
23 × 17 = 136
22 × 5 × 7 = 140
2 × 3 × 52 = 150
23 × 19 = 152
22 × 3 × 13 = 156
23 × 3 × 7 = 168
2 × 5 × 17 = 170
52 × 7 = 175
2 × 7 × 13 = 182
2 × 5 × 19 = 190
3 × 5 × 13 = 195
23 × 52 = 200
22 × 3 × 17 = 204
2 × 3 × 5 × 7 = 210
13 × 17 = 221
22 × 3 × 19 = 228
2 × 7 × 17 = 238
13 × 19 = 247
3 × 5 × 17 = 255
22 × 5 × 13 = 260
2 × 7 × 19 = 266
3 × 7 × 13 = 273
23 × 5 × 7 = 280
3 × 5 × 19 = 285
22 × 3 × 52 = 300
23 × 3 × 13 = 312
17 × 19 = 323
52 × 13 = 325
22 × 5 × 17 = 340
2 × 52 × 7 = 350
3 × 7 × 17 = 357
22 × 7 × 13 = 364
22 × 5 × 19 = 380
2 × 3 × 5 × 13 = 390
3 × 7 × 19 = 399
23 × 3 × 17 = 408
22 × 3 × 5 × 7 = 420
52 × 17 = 425
2 × 13 × 17 = 442
5 × 7 × 13 = 455
23 × 3 × 19 = 456
52 × 19 = 475
22 × 7 × 17 = 476
2 × 13 × 19 = 494
2 × 3 × 5 × 17 = 510
23 × 5 × 13 = 520
3 × 52 × 7 = 525
22 × 7 × 19 = 532
2 × 3 × 7 × 13 = 546
2 × 3 × 5 × 19 = 570
5 × 7 × 17 = 595
23 × 3 × 52 = 600
2 × 17 × 19 = 646
2 × 52 × 13 = 650
3 × 13 × 17 = 663
5 × 7 × 19 = 665
23 × 5 × 17 = 680
22 × 52 × 7 = 700
2 × 3 × 7 × 17 = 714
23 × 7 × 13 = 728
3 × 13 × 19 = 741
23 × 5 × 19 = 760
22 × 3 × 5 × 13 = 780
2 × 3 × 7 × 19 = 798
23 × 3 × 5 × 7 = 840
2 × 52 × 17 = 850
22 × 13 × 17 = 884
2 × 5 × 7 × 13 = 910
2 × 52 × 19 = 950
23 × 7 × 17 = 952
3 × 17 × 19 = 969
3 × 52 × 13 = 975
22 × 13 × 19 = 988
22 × 3 × 5 × 17 = 1,020
2 × 3 × 52 × 7 = 1,050
23 × 7 × 19 = 1,064
22 × 3 × 7 × 13 = 1,092
5 × 13 × 17 = 1,105
22 × 3 × 5 × 19 = 1,140
2 × 5 × 7 × 17 = 1,190
5 × 13 × 19 = 1,235
3 × 52 × 17 = 1,275
22 × 17 × 19 = 1,292
22 × 52 × 13 = 1,300
2 × 3 × 13 × 17 = 1,326
2 × 5 × 7 × 19 = 1,330
3 × 5 × 7 × 13 = 1,365
23 × 52 × 7 = 1,400
3 × 52 × 19 = 1,425
22 × 3 × 7 × 17 = 1,428
2 × 3 × 13 × 19 = 1,482
7 × 13 × 17 = 1,547
23 × 3 × 5 × 13 = 1,560
22 × 3 × 7 × 19 = 1,596
5 × 17 × 19 = 1,615
22 × 52 × 17 = 1,700
7 × 13 × 19 = 1,729
23 × 13 × 17 = 1,768
3 × 5 × 7 × 17 = 1,785
22 × 5 × 7 × 13 = 1,820
22 × 52 × 19 = 1,900
2 × 3 × 17 × 19 = 1,938
2 × 3 × 52 × 13 = 1,950
23 × 13 × 19 = 1,976
3 × 5 × 7 × 19 = 1,995
23 × 3 × 5 × 17 = 2,040
22 × 3 × 52 × 7 = 2,100
23 × 3 × 7 × 13 = 2,184
2 × 5 × 13 × 17 = 2,210
7 × 17 × 19 = 2,261
52 × 7 × 13 = 2,275
23 × 3 × 5 × 19 = 2,280
22 × 5 × 7 × 17 = 2,380
2 × 5 × 13 × 19 = 2,470
2 × 3 × 52 × 17 = 2,550
23 × 17 × 19 = 2,584
23 × 52 × 13 = 2,600
22 × 3 × 13 × 17 = 2,652
22 × 5 × 7 × 19 = 2,660
2 × 3 × 5 × 7 × 13 = 2,730
2 × 3 × 52 × 19 = 2,850
23 × 3 × 7 × 17 = 2,856
22 × 3 × 13 × 19 = 2,964
52 × 7 × 17 = 2,975
2 × 7 × 13 × 17 = 3,094
23 × 3 × 7 × 19 = 3,192
2 × 5 × 17 × 19 = 3,230
3 × 5 × 13 × 17 = 3,315
52 × 7 × 19 = 3,325
23 × 52 × 17 = 3,400
2 × 7 × 13 × 19 = 3,458
2 × 3 × 5 × 7 × 17 = 3,570
23 × 5 × 7 × 13 = 3,640
3 × 5 × 13 × 19 = 3,705
23 × 52 × 19 = 3,800
22 × 3 × 17 × 19 = 3,876
22 × 3 × 52 × 13 = 3,900
2 × 3 × 5 × 7 × 19 = 3,990
13 × 17 × 19 = 4,199
This list continues below...

... This list continues from above
23 × 3 × 52 × 7 = 4,200
22 × 5 × 13 × 17 = 4,420
2 × 7 × 17 × 19 = 4,522
2 × 52 × 7 × 13 = 4,550
3 × 7 × 13 × 17 = 4,641
23 × 5 × 7 × 17 = 4,760
3 × 5 × 17 × 19 = 4,845
22 × 5 × 13 × 19 = 4,940
22 × 3 × 52 × 17 = 5,100
3 × 7 × 13 × 19 = 5,187
23 × 3 × 13 × 17 = 5,304
23 × 5 × 7 × 19 = 5,320
22 × 3 × 5 × 7 × 13 = 5,460
52 × 13 × 17 = 5,525
22 × 3 × 52 × 19 = 5,700
23 × 3 × 13 × 19 = 5,928
2 × 52 × 7 × 17 = 5,950
52 × 13 × 19 = 6,175
22 × 7 × 13 × 17 = 6,188
22 × 5 × 17 × 19 = 6,460
2 × 3 × 5 × 13 × 17 = 6,630
2 × 52 × 7 × 19 = 6,650
3 × 7 × 17 × 19 = 6,783
3 × 52 × 7 × 13 = 6,825
22 × 7 × 13 × 19 = 6,916
22 × 3 × 5 × 7 × 17 = 7,140
2 × 3 × 5 × 13 × 19 = 7,410
5 × 7 × 13 × 17 = 7,735
23 × 3 × 17 × 19 = 7,752
23 × 3 × 52 × 13 = 7,800
22 × 3 × 5 × 7 × 19 = 7,980
52 × 17 × 19 = 8,075
2 × 13 × 17 × 19 = 8,398
5 × 7 × 13 × 19 = 8,645
23 × 5 × 13 × 17 = 8,840
3 × 52 × 7 × 17 = 8,925
22 × 7 × 17 × 19 = 9,044
22 × 52 × 7 × 13 = 9,100
2 × 3 × 7 × 13 × 17 = 9,282
2 × 3 × 5 × 17 × 19 = 9,690
23 × 5 × 13 × 19 = 9,880
3 × 52 × 7 × 19 = 9,975
23 × 3 × 52 × 17 = 10,200
2 × 3 × 7 × 13 × 19 = 10,374
23 × 3 × 5 × 7 × 13 = 10,920
2 × 52 × 13 × 17 = 11,050
5 × 7 × 17 × 19 = 11,305
23 × 3 × 52 × 19 = 11,400
22 × 52 × 7 × 17 = 11,900
2 × 52 × 13 × 19 = 12,350
23 × 7 × 13 × 17 = 12,376
3 × 13 × 17 × 19 = 12,597
23 × 5 × 17 × 19 = 12,920
22 × 3 × 5 × 13 × 17 = 13,260
22 × 52 × 7 × 19 = 13,300
2 × 3 × 7 × 17 × 19 = 13,566
2 × 3 × 52 × 7 × 13 = 13,650
23 × 7 × 13 × 19 = 13,832
23 × 3 × 5 × 7 × 17 = 14,280
22 × 3 × 5 × 13 × 19 = 14,820
2 × 5 × 7 × 13 × 17 = 15,470
23 × 3 × 5 × 7 × 19 = 15,960
2 × 52 × 17 × 19 = 16,150
3 × 52 × 13 × 17 = 16,575
22 × 13 × 17 × 19 = 16,796
2 × 5 × 7 × 13 × 19 = 17,290
2 × 3 × 52 × 7 × 17 = 17,850
23 × 7 × 17 × 19 = 18,088
23 × 52 × 7 × 13 = 18,200
3 × 52 × 13 × 19 = 18,525
22 × 3 × 7 × 13 × 17 = 18,564
22 × 3 × 5 × 17 × 19 = 19,380
2 × 3 × 52 × 7 × 19 = 19,950
22 × 3 × 7 × 13 × 19 = 20,748
5 × 13 × 17 × 19 = 20,995
22 × 52 × 13 × 17 = 22,100
2 × 5 × 7 × 17 × 19 = 22,610
3 × 5 × 7 × 13 × 17 = 23,205
23 × 52 × 7 × 17 = 23,800
3 × 52 × 17 × 19 = 24,225
22 × 52 × 13 × 19 = 24,700
2 × 3 × 13 × 17 × 19 = 25,194
3 × 5 × 7 × 13 × 19 = 25,935
23 × 3 × 5 × 13 × 17 = 26,520
23 × 52 × 7 × 19 = 26,600
22 × 3 × 7 × 17 × 19 = 27,132
22 × 3 × 52 × 7 × 13 = 27,300
7 × 13 × 17 × 19 = 29,393
23 × 3 × 5 × 13 × 19 = 29,640
22 × 5 × 7 × 13 × 17 = 30,940
22 × 52 × 17 × 19 = 32,300
2 × 3 × 52 × 13 × 17 = 33,150
23 × 13 × 17 × 19 = 33,592
3 × 5 × 7 × 17 × 19 = 33,915
22 × 5 × 7 × 13 × 19 = 34,580
22 × 3 × 52 × 7 × 17 = 35,700
2 × 3 × 52 × 13 × 19 = 37,050
23 × 3 × 7 × 13 × 17 = 37,128
52 × 7 × 13 × 17 = 38,675
23 × 3 × 5 × 17 × 19 = 38,760
22 × 3 × 52 × 7 × 19 = 39,900
23 × 3 × 7 × 13 × 19 = 41,496
2 × 5 × 13 × 17 × 19 = 41,990
52 × 7 × 13 × 19 = 43,225
23 × 52 × 13 × 17 = 44,200
22 × 5 × 7 × 17 × 19 = 45,220
2 × 3 × 5 × 7 × 13 × 17 = 46,410
2 × 3 × 52 × 17 × 19 = 48,450
23 × 52 × 13 × 19 = 49,400
22 × 3 × 13 × 17 × 19 = 50,388
2 × 3 × 5 × 7 × 13 × 19 = 51,870
23 × 3 × 7 × 17 × 19 = 54,264
23 × 3 × 52 × 7 × 13 = 54,600
52 × 7 × 17 × 19 = 56,525
2 × 7 × 13 × 17 × 19 = 58,786
23 × 5 × 7 × 13 × 17 = 61,880
3 × 5 × 13 × 17 × 19 = 62,985
23 × 52 × 17 × 19 = 64,600
22 × 3 × 52 × 13 × 17 = 66,300
2 × 3 × 5 × 7 × 17 × 19 = 67,830
23 × 5 × 7 × 13 × 19 = 69,160
23 × 3 × 52 × 7 × 17 = 71,400
22 × 3 × 52 × 13 × 19 = 74,100
2 × 52 × 7 × 13 × 17 = 77,350
23 × 3 × 52 × 7 × 19 = 79,800
22 × 5 × 13 × 17 × 19 = 83,980
2 × 52 × 7 × 13 × 19 = 86,450
3 × 7 × 13 × 17 × 19 = 88,179
23 × 5 × 7 × 17 × 19 = 90,440
22 × 3 × 5 × 7 × 13 × 17 = 92,820
22 × 3 × 52 × 17 × 19 = 96,900
23 × 3 × 13 × 17 × 19 = 100,776
22 × 3 × 5 × 7 × 13 × 19 = 103,740
52 × 13 × 17 × 19 = 104,975
2 × 52 × 7 × 17 × 19 = 113,050
3 × 52 × 7 × 13 × 17 = 116,025
22 × 7 × 13 × 17 × 19 = 117,572
2 × 3 × 5 × 13 × 17 × 19 = 125,970
3 × 52 × 7 × 13 × 19 = 129,675
23 × 3 × 52 × 13 × 17 = 132,600
22 × 3 × 5 × 7 × 17 × 19 = 135,660
5 × 7 × 13 × 17 × 19 = 146,965
23 × 3 × 52 × 13 × 19 = 148,200
22 × 52 × 7 × 13 × 17 = 154,700
23 × 5 × 13 × 17 × 19 = 167,960
3 × 52 × 7 × 17 × 19 = 169,575
22 × 52 × 7 × 13 × 19 = 172,900
2 × 3 × 7 × 13 × 17 × 19 = 176,358
23 × 3 × 5 × 7 × 13 × 17 = 185,640
23 × 3 × 52 × 17 × 19 = 193,800
23 × 3 × 5 × 7 × 13 × 19 = 207,480
2 × 52 × 13 × 17 × 19 = 209,950
22 × 52 × 7 × 17 × 19 = 226,100
2 × 3 × 52 × 7 × 13 × 17 = 232,050
23 × 7 × 13 × 17 × 19 = 235,144
22 × 3 × 5 × 13 × 17 × 19 = 251,940
2 × 3 × 52 × 7 × 13 × 19 = 259,350
23 × 3 × 5 × 7 × 17 × 19 = 271,320
2 × 5 × 7 × 13 × 17 × 19 = 293,930
23 × 52 × 7 × 13 × 17 = 309,400
3 × 52 × 13 × 17 × 19 = 314,925
2 × 3 × 52 × 7 × 17 × 19 = 339,150
23 × 52 × 7 × 13 × 19 = 345,800
22 × 3 × 7 × 13 × 17 × 19 = 352,716
22 × 52 × 13 × 17 × 19 = 419,900
3 × 5 × 7 × 13 × 17 × 19 = 440,895
23 × 52 × 7 × 17 × 19 = 452,200
22 × 3 × 52 × 7 × 13 × 17 = 464,100
23 × 3 × 5 × 13 × 17 × 19 = 503,880
22 × 3 × 52 × 7 × 13 × 19 = 518,700
22 × 5 × 7 × 13 × 17 × 19 = 587,860
2 × 3 × 52 × 13 × 17 × 19 = 629,850
22 × 3 × 52 × 7 × 17 × 19 = 678,300
23 × 3 × 7 × 13 × 17 × 19 = 705,432
52 × 7 × 13 × 17 × 19 = 734,825
23 × 52 × 13 × 17 × 19 = 839,800
2 × 3 × 5 × 7 × 13 × 17 × 19 = 881,790
23 × 3 × 52 × 7 × 13 × 17 = 928,200
23 × 3 × 52 × 7 × 13 × 19 = 1,037,400
23 × 5 × 7 × 13 × 17 × 19 = 1,175,720
22 × 3 × 52 × 13 × 17 × 19 = 1,259,700
23 × 3 × 52 × 7 × 17 × 19 = 1,356,600
2 × 52 × 7 × 13 × 17 × 19 = 1,469,650
22 × 3 × 5 × 7 × 13 × 17 × 19 = 1,763,580
3 × 52 × 7 × 13 × 17 × 19 = 2,204,475
23 × 3 × 52 × 13 × 17 × 19 = 2,519,400
22 × 52 × 7 × 13 × 17 × 19 = 2,939,300
23 × 3 × 5 × 7 × 13 × 17 × 19 = 3,527,160
2 × 3 × 52 × 7 × 13 × 17 × 19 = 4,408,950
23 × 52 × 7 × 13 × 17 × 19 = 5,878,600
22 × 3 × 52 × 7 × 13 × 17 × 19 = 8,817,900
23 × 3 × 52 × 7 × 13 × 17 × 19 = 17,635,800

The final answer:
(scroll down)

17,635,800 has 384 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 8; 10; 12; 13; 14; 15; 17; 19; 20; 21; 24; 25; 26; 28; 30; 34; 35; 38; 39; 40; 42; 50; 51; 52; 56; 57; 60; 65; 68; 70; 75; 76; 78; 84; 85; 91; 95; 100; 102; 104; 105; 114; 119; 120; 130; 133; 136; 140; 150; 152; 156; 168; 170; 175; 182; 190; 195; 200; 204; 210; 221; 228; 238; 247; 255; 260; 266; 273; 280; 285; 300; 312; 323; 325; 340; 350; 357; 364; 380; 390; 399; 408; 420; 425; 442; 455; 456; 475; 476; 494; 510; 520; 525; 532; 546; 570; 595; 600; 646; 650; 663; 665; 680; 700; 714; 728; 741; 760; 780; 798; 840; 850; 884; 910; 950; 952; 969; 975; 988; 1,020; 1,050; 1,064; 1,092; 1,105; 1,140; 1,190; 1,235; 1,275; 1,292; 1,300; 1,326; 1,330; 1,365; 1,400; 1,425; 1,428; 1,482; 1,547; 1,560; 1,596; 1,615; 1,700; 1,729; 1,768; 1,785; 1,820; 1,900; 1,938; 1,950; 1,976; 1,995; 2,040; 2,100; 2,184; 2,210; 2,261; 2,275; 2,280; 2,380; 2,470; 2,550; 2,584; 2,600; 2,652; 2,660; 2,730; 2,850; 2,856; 2,964; 2,975; 3,094; 3,192; 3,230; 3,315; 3,325; 3,400; 3,458; 3,570; 3,640; 3,705; 3,800; 3,876; 3,900; 3,990; 4,199; 4,200; 4,420; 4,522; 4,550; 4,641; 4,760; 4,845; 4,940; 5,100; 5,187; 5,304; 5,320; 5,460; 5,525; 5,700; 5,928; 5,950; 6,175; 6,188; 6,460; 6,630; 6,650; 6,783; 6,825; 6,916; 7,140; 7,410; 7,735; 7,752; 7,800; 7,980; 8,075; 8,398; 8,645; 8,840; 8,925; 9,044; 9,100; 9,282; 9,690; 9,880; 9,975; 10,200; 10,374; 10,920; 11,050; 11,305; 11,400; 11,900; 12,350; 12,376; 12,597; 12,920; 13,260; 13,300; 13,566; 13,650; 13,832; 14,280; 14,820; 15,470; 15,960; 16,150; 16,575; 16,796; 17,290; 17,850; 18,088; 18,200; 18,525; 18,564; 19,380; 19,950; 20,748; 20,995; 22,100; 22,610; 23,205; 23,800; 24,225; 24,700; 25,194; 25,935; 26,520; 26,600; 27,132; 27,300; 29,393; 29,640; 30,940; 32,300; 33,150; 33,592; 33,915; 34,580; 35,700; 37,050; 37,128; 38,675; 38,760; 39,900; 41,496; 41,990; 43,225; 44,200; 45,220; 46,410; 48,450; 49,400; 50,388; 51,870; 54,264; 54,600; 56,525; 58,786; 61,880; 62,985; 64,600; 66,300; 67,830; 69,160; 71,400; 74,100; 77,350; 79,800; 83,980; 86,450; 88,179; 90,440; 92,820; 96,900; 100,776; 103,740; 104,975; 113,050; 116,025; 117,572; 125,970; 129,675; 132,600; 135,660; 146,965; 148,200; 154,700; 167,960; 169,575; 172,900; 176,358; 185,640; 193,800; 207,480; 209,950; 226,100; 232,050; 235,144; 251,940; 259,350; 271,320; 293,930; 309,400; 314,925; 339,150; 345,800; 352,716; 419,900; 440,895; 452,200; 464,100; 503,880; 518,700; 587,860; 629,850; 678,300; 705,432; 734,825; 839,800; 881,790; 928,200; 1,037,400; 1,175,720; 1,259,700; 1,356,600; 1,469,650; 1,763,580; 2,204,475; 2,519,400; 2,939,300; 3,527,160; 4,408,950; 5,878,600; 8,817,900 and 17,635,800
out of which 7 prime factors: 2; 3; 5; 7; 13; 17 and 19
17,635,800 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.


Other similar operations of calculating factors (divisors):

» What are all the proper, improper and prime factors (divisors) of the number 17,635,796?

» What are all the proper, improper and prime factors (divisors) of the number 17,635,804?


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

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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".