Given the Number 19,999,980 Calculate (Find) All Its Factors (Divisors – the Proper, the Improper and the Prime Factors). Online Calculator

All the factors (divisors) of the number 19,999,980

1. Carry out the prime factorization of the number 19,999,980:

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


19,999,980 = 22 × 33 × 5 × 7 × 11 × 13 × 37
19,999,980 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 19,999,980

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
32 = 9
2 × 5 = 10
prime factor = 11
22 × 3 = 12
prime factor = 13
2 × 7 = 14
3 × 5 = 15
2 × 32 = 18
22 × 5 = 20
3 × 7 = 21
2 × 11 = 22
2 × 13 = 26
33 = 27
22 × 7 = 28
2 × 3 × 5 = 30
3 × 11 = 33
5 × 7 = 35
22 × 32 = 36
prime factor = 37
3 × 13 = 39
2 × 3 × 7 = 42
22 × 11 = 44
32 × 5 = 45
22 × 13 = 52
2 × 33 = 54
5 × 11 = 55
22 × 3 × 5 = 60
32 × 7 = 63
5 × 13 = 65
2 × 3 × 11 = 66
2 × 5 × 7 = 70
2 × 37 = 74
7 × 11 = 77
2 × 3 × 13 = 78
22 × 3 × 7 = 84
2 × 32 × 5 = 90
7 × 13 = 91
32 × 11 = 99
3 × 5 × 7 = 105
22 × 33 = 108
2 × 5 × 11 = 110
3 × 37 = 111
32 × 13 = 117
2 × 32 × 7 = 126
2 × 5 × 13 = 130
22 × 3 × 11 = 132
33 × 5 = 135
22 × 5 × 7 = 140
11 × 13 = 143
22 × 37 = 148
2 × 7 × 11 = 154
22 × 3 × 13 = 156
3 × 5 × 11 = 165
22 × 32 × 5 = 180
2 × 7 × 13 = 182
5 × 37 = 185
33 × 7 = 189
3 × 5 × 13 = 195
2 × 32 × 11 = 198
2 × 3 × 5 × 7 = 210
22 × 5 × 11 = 220
2 × 3 × 37 = 222
3 × 7 × 11 = 231
2 × 32 × 13 = 234
22 × 32 × 7 = 252
7 × 37 = 259
22 × 5 × 13 = 260
2 × 33 × 5 = 270
3 × 7 × 13 = 273
2 × 11 × 13 = 286
33 × 11 = 297
22 × 7 × 11 = 308
32 × 5 × 7 = 315
2 × 3 × 5 × 11 = 330
32 × 37 = 333
33 × 13 = 351
22 × 7 × 13 = 364
2 × 5 × 37 = 370
2 × 33 × 7 = 378
5 × 7 × 11 = 385
2 × 3 × 5 × 13 = 390
22 × 32 × 11 = 396
11 × 37 = 407
22 × 3 × 5 × 7 = 420
3 × 11 × 13 = 429
22 × 3 × 37 = 444
5 × 7 × 13 = 455
2 × 3 × 7 × 11 = 462
22 × 32 × 13 = 468
13 × 37 = 481
32 × 5 × 11 = 495
2 × 7 × 37 = 518
22 × 33 × 5 = 540
2 × 3 × 7 × 13 = 546
3 × 5 × 37 = 555
22 × 11 × 13 = 572
32 × 5 × 13 = 585
2 × 33 × 11 = 594
2 × 32 × 5 × 7 = 630
22 × 3 × 5 × 11 = 660
2 × 32 × 37 = 666
32 × 7 × 11 = 693
2 × 33 × 13 = 702
5 × 11 × 13 = 715
22 × 5 × 37 = 740
22 × 33 × 7 = 756
2 × 5 × 7 × 11 = 770
3 × 7 × 37 = 777
22 × 3 × 5 × 13 = 780
2 × 11 × 37 = 814
32 × 7 × 13 = 819
2 × 3 × 11 × 13 = 858
2 × 5 × 7 × 13 = 910
22 × 3 × 7 × 11 = 924
33 × 5 × 7 = 945
2 × 13 × 37 = 962
2 × 32 × 5 × 11 = 990
33 × 37 = 999
7 × 11 × 13 = 1,001
22 × 7 × 37 = 1,036
22 × 3 × 7 × 13 = 1,092
2 × 3 × 5 × 37 = 1,110
3 × 5 × 7 × 11 = 1,155
2 × 32 × 5 × 13 = 1,170
22 × 33 × 11 = 1,188
3 × 11 × 37 = 1,221
22 × 32 × 5 × 7 = 1,260
32 × 11 × 13 = 1,287
5 × 7 × 37 = 1,295
22 × 32 × 37 = 1,332
3 × 5 × 7 × 13 = 1,365
2 × 32 × 7 × 11 = 1,386
22 × 33 × 13 = 1,404
2 × 5 × 11 × 13 = 1,430
3 × 13 × 37 = 1,443
33 × 5 × 11 = 1,485
22 × 5 × 7 × 11 = 1,540
2 × 3 × 7 × 37 = 1,554
22 × 11 × 37 = 1,628
2 × 32 × 7 × 13 = 1,638
32 × 5 × 37 = 1,665
22 × 3 × 11 × 13 = 1,716
33 × 5 × 13 = 1,755
22 × 5 × 7 × 13 = 1,820
2 × 33 × 5 × 7 = 1,890
22 × 13 × 37 = 1,924
22 × 32 × 5 × 11 = 1,980
2 × 33 × 37 = 1,998
2 × 7 × 11 × 13 = 2,002
5 × 11 × 37 = 2,035
33 × 7 × 11 = 2,079
3 × 5 × 11 × 13 = 2,145
22 × 3 × 5 × 37 = 2,220
2 × 3 × 5 × 7 × 11 = 2,310
32 × 7 × 37 = 2,331
22 × 32 × 5 × 13 = 2,340
5 × 13 × 37 = 2,405
2 × 3 × 11 × 37 = 2,442
33 × 7 × 13 = 2,457
2 × 32 × 11 × 13 = 2,574
2 × 5 × 7 × 37 = 2,590
2 × 3 × 5 × 7 × 13 = 2,730
22 × 32 × 7 × 11 = 2,772
7 × 11 × 37 = 2,849
22 × 5 × 11 × 13 = 2,860
2 × 3 × 13 × 37 = 2,886
2 × 33 × 5 × 11 = 2,970
3 × 7 × 11 × 13 = 3,003
22 × 3 × 7 × 37 = 3,108
22 × 32 × 7 × 13 = 3,276
2 × 32 × 5 × 37 = 3,330
7 × 13 × 37 = 3,367
32 × 5 × 7 × 11 = 3,465
2 × 33 × 5 × 13 = 3,510
32 × 11 × 37 = 3,663
22 × 33 × 5 × 7 = 3,780
33 × 11 × 13 = 3,861
3 × 5 × 7 × 37 = 3,885
22 × 33 × 37 = 3,996
22 × 7 × 11 × 13 = 4,004
2 × 5 × 11 × 37 = 4,070
32 × 5 × 7 × 13 = 4,095
2 × 33 × 7 × 11 = 4,158
2 × 3 × 5 × 11 × 13 = 4,290
32 × 13 × 37 = 4,329
This list continues below...

... This list continues from above
22 × 3 × 5 × 7 × 11 = 4,620
2 × 32 × 7 × 37 = 4,662
2 × 5 × 13 × 37 = 4,810
22 × 3 × 11 × 37 = 4,884
2 × 33 × 7 × 13 = 4,914
33 × 5 × 37 = 4,995
5 × 7 × 11 × 13 = 5,005
22 × 32 × 11 × 13 = 5,148
22 × 5 × 7 × 37 = 5,180
11 × 13 × 37 = 5,291
22 × 3 × 5 × 7 × 13 = 5,460
2 × 7 × 11 × 37 = 5,698
22 × 3 × 13 × 37 = 5,772
22 × 33 × 5 × 11 = 5,940
2 × 3 × 7 × 11 × 13 = 6,006
3 × 5 × 11 × 37 = 6,105
32 × 5 × 11 × 13 = 6,435
22 × 32 × 5 × 37 = 6,660
2 × 7 × 13 × 37 = 6,734
2 × 32 × 5 × 7 × 11 = 6,930
33 × 7 × 37 = 6,993
22 × 33 × 5 × 13 = 7,020
3 × 5 × 13 × 37 = 7,215
2 × 32 × 11 × 37 = 7,326
2 × 33 × 11 × 13 = 7,722
2 × 3 × 5 × 7 × 37 = 7,770
22 × 5 × 11 × 37 = 8,140
2 × 32 × 5 × 7 × 13 = 8,190
22 × 33 × 7 × 11 = 8,316
3 × 7 × 11 × 37 = 8,547
22 × 3 × 5 × 11 × 13 = 8,580
2 × 32 × 13 × 37 = 8,658
32 × 7 × 11 × 13 = 9,009
22 × 32 × 7 × 37 = 9,324
22 × 5 × 13 × 37 = 9,620
22 × 33 × 7 × 13 = 9,828
2 × 33 × 5 × 37 = 9,990
2 × 5 × 7 × 11 × 13 = 10,010
3 × 7 × 13 × 37 = 10,101
33 × 5 × 7 × 11 = 10,395
2 × 11 × 13 × 37 = 10,582
33 × 11 × 37 = 10,989
22 × 7 × 11 × 37 = 11,396
32 × 5 × 7 × 37 = 11,655
22 × 3 × 7 × 11 × 13 = 12,012
2 × 3 × 5 × 11 × 37 = 12,210
33 × 5 × 7 × 13 = 12,285
2 × 32 × 5 × 11 × 13 = 12,870
33 × 13 × 37 = 12,987
22 × 7 × 13 × 37 = 13,468
22 × 32 × 5 × 7 × 11 = 13,860
2 × 33 × 7 × 37 = 13,986
5 × 7 × 11 × 37 = 14,245
2 × 3 × 5 × 13 × 37 = 14,430
22 × 32 × 11 × 37 = 14,652
3 × 5 × 7 × 11 × 13 = 15,015
22 × 33 × 11 × 13 = 15,444
22 × 3 × 5 × 7 × 37 = 15,540
3 × 11 × 13 × 37 = 15,873
22 × 32 × 5 × 7 × 13 = 16,380
5 × 7 × 13 × 37 = 16,835
2 × 3 × 7 × 11 × 37 = 17,094
22 × 32 × 13 × 37 = 17,316
2 × 32 × 7 × 11 × 13 = 18,018
32 × 5 × 11 × 37 = 18,315
33 × 5 × 11 × 13 = 19,305
22 × 33 × 5 × 37 = 19,980
22 × 5 × 7 × 11 × 13 = 20,020
2 × 3 × 7 × 13 × 37 = 20,202
2 × 33 × 5 × 7 × 11 = 20,790
22 × 11 × 13 × 37 = 21,164
32 × 5 × 13 × 37 = 21,645
2 × 33 × 11 × 37 = 21,978
2 × 32 × 5 × 7 × 37 = 23,310
22 × 3 × 5 × 11 × 37 = 24,420
2 × 33 × 5 × 7 × 13 = 24,570
32 × 7 × 11 × 37 = 25,641
22 × 32 × 5 × 11 × 13 = 25,740
2 × 33 × 13 × 37 = 25,974
5 × 11 × 13 × 37 = 26,455
33 × 7 × 11 × 13 = 27,027
22 × 33 × 7 × 37 = 27,972
2 × 5 × 7 × 11 × 37 = 28,490
22 × 3 × 5 × 13 × 37 = 28,860
2 × 3 × 5 × 7 × 11 × 13 = 30,030
32 × 7 × 13 × 37 = 30,303
2 × 3 × 11 × 13 × 37 = 31,746
2 × 5 × 7 × 13 × 37 = 33,670
22 × 3 × 7 × 11 × 37 = 34,188
33 × 5 × 7 × 37 = 34,965
22 × 32 × 7 × 11 × 13 = 36,036
2 × 32 × 5 × 11 × 37 = 36,630
7 × 11 × 13 × 37 = 37,037
2 × 33 × 5 × 11 × 13 = 38,610
22 × 3 × 7 × 13 × 37 = 40,404
22 × 33 × 5 × 7 × 11 = 41,580
3 × 5 × 7 × 11 × 37 = 42,735
2 × 32 × 5 × 13 × 37 = 43,290
22 × 33 × 11 × 37 = 43,956
32 × 5 × 7 × 11 × 13 = 45,045
22 × 32 × 5 × 7 × 37 = 46,620
32 × 11 × 13 × 37 = 47,619
22 × 33 × 5 × 7 × 13 = 49,140
3 × 5 × 7 × 13 × 37 = 50,505
2 × 32 × 7 × 11 × 37 = 51,282
22 × 33 × 13 × 37 = 51,948
2 × 5 × 11 × 13 × 37 = 52,910
2 × 33 × 7 × 11 × 13 = 54,054
33 × 5 × 11 × 37 = 54,945
22 × 5 × 7 × 11 × 37 = 56,980
22 × 3 × 5 × 7 × 11 × 13 = 60,060
2 × 32 × 7 × 13 × 37 = 60,606
22 × 3 × 11 × 13 × 37 = 63,492
33 × 5 × 13 × 37 = 64,935
22 × 5 × 7 × 13 × 37 = 67,340
2 × 33 × 5 × 7 × 37 = 69,930
22 × 32 × 5 × 11 × 37 = 73,260
2 × 7 × 11 × 13 × 37 = 74,074
33 × 7 × 11 × 37 = 76,923
22 × 33 × 5 × 11 × 13 = 77,220
3 × 5 × 11 × 13 × 37 = 79,365
2 × 3 × 5 × 7 × 11 × 37 = 85,470
22 × 32 × 5 × 13 × 37 = 86,580
2 × 32 × 5 × 7 × 11 × 13 = 90,090
33 × 7 × 13 × 37 = 90,909
2 × 32 × 11 × 13 × 37 = 95,238
2 × 3 × 5 × 7 × 13 × 37 = 101,010
22 × 32 × 7 × 11 × 37 = 102,564
22 × 5 × 11 × 13 × 37 = 105,820
22 × 33 × 7 × 11 × 13 = 108,108
2 × 33 × 5 × 11 × 37 = 109,890
3 × 7 × 11 × 13 × 37 = 111,111
22 × 32 × 7 × 13 × 37 = 121,212
32 × 5 × 7 × 11 × 37 = 128,205
2 × 33 × 5 × 13 × 37 = 129,870
33 × 5 × 7 × 11 × 13 = 135,135
22 × 33 × 5 × 7 × 37 = 139,860
33 × 11 × 13 × 37 = 142,857
22 × 7 × 11 × 13 × 37 = 148,148
32 × 5 × 7 × 13 × 37 = 151,515
2 × 33 × 7 × 11 × 37 = 153,846
2 × 3 × 5 × 11 × 13 × 37 = 158,730
22 × 3 × 5 × 7 × 11 × 37 = 170,940
22 × 32 × 5 × 7 × 11 × 13 = 180,180
2 × 33 × 7 × 13 × 37 = 181,818
5 × 7 × 11 × 13 × 37 = 185,185
22 × 32 × 11 × 13 × 37 = 190,476
22 × 3 × 5 × 7 × 13 × 37 = 202,020
22 × 33 × 5 × 11 × 37 = 219,780
2 × 3 × 7 × 11 × 13 × 37 = 222,222
32 × 5 × 11 × 13 × 37 = 238,095
2 × 32 × 5 × 7 × 11 × 37 = 256,410
22 × 33 × 5 × 13 × 37 = 259,740
2 × 33 × 5 × 7 × 11 × 13 = 270,270
2 × 33 × 11 × 13 × 37 = 285,714
2 × 32 × 5 × 7 × 13 × 37 = 303,030
22 × 33 × 7 × 11 × 37 = 307,692
22 × 3 × 5 × 11 × 13 × 37 = 317,460
32 × 7 × 11 × 13 × 37 = 333,333
22 × 33 × 7 × 13 × 37 = 363,636
2 × 5 × 7 × 11 × 13 × 37 = 370,370
33 × 5 × 7 × 11 × 37 = 384,615
22 × 3 × 7 × 11 × 13 × 37 = 444,444
33 × 5 × 7 × 13 × 37 = 454,545
2 × 32 × 5 × 11 × 13 × 37 = 476,190
22 × 32 × 5 × 7 × 11 × 37 = 512,820
22 × 33 × 5 × 7 × 11 × 13 = 540,540
3 × 5 × 7 × 11 × 13 × 37 = 555,555
22 × 33 × 11 × 13 × 37 = 571,428
22 × 32 × 5 × 7 × 13 × 37 = 606,060
2 × 32 × 7 × 11 × 13 × 37 = 666,666
33 × 5 × 11 × 13 × 37 = 714,285
22 × 5 × 7 × 11 × 13 × 37 = 740,740
2 × 33 × 5 × 7 × 11 × 37 = 769,230
2 × 33 × 5 × 7 × 13 × 37 = 909,090
22 × 32 × 5 × 11 × 13 × 37 = 952,380
33 × 7 × 11 × 13 × 37 = 999,999
2 × 3 × 5 × 7 × 11 × 13 × 37 = 1,111,110
22 × 32 × 7 × 11 × 13 × 37 = 1,333,332
2 × 33 × 5 × 11 × 13 × 37 = 1,428,570
22 × 33 × 5 × 7 × 11 × 37 = 1,538,460
32 × 5 × 7 × 11 × 13 × 37 = 1,666,665
22 × 33 × 5 × 7 × 13 × 37 = 1,818,180
2 × 33 × 7 × 11 × 13 × 37 = 1,999,998
22 × 3 × 5 × 7 × 11 × 13 × 37 = 2,222,220
22 × 33 × 5 × 11 × 13 × 37 = 2,857,140
2 × 32 × 5 × 7 × 11 × 13 × 37 = 3,333,330
22 × 33 × 7 × 11 × 13 × 37 = 3,999,996
33 × 5 × 7 × 11 × 13 × 37 = 4,999,995
22 × 32 × 5 × 7 × 11 × 13 × 37 = 6,666,660
2 × 33 × 5 × 7 × 11 × 13 × 37 = 9,999,990
22 × 33 × 5 × 7 × 11 × 13 × 37 = 19,999,980

The final answer:
(scroll down)

19,999,980 has 384 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 9; 10; 11; 12; 13; 14; 15; 18; 20; 21; 22; 26; 27; 28; 30; 33; 35; 36; 37; 39; 42; 44; 45; 52; 54; 55; 60; 63; 65; 66; 70; 74; 77; 78; 84; 90; 91; 99; 105; 108; 110; 111; 117; 126; 130; 132; 135; 140; 143; 148; 154; 156; 165; 180; 182; 185; 189; 195; 198; 210; 220; 222; 231; 234; 252; 259; 260; 270; 273; 286; 297; 308; 315; 330; 333; 351; 364; 370; 378; 385; 390; 396; 407; 420; 429; 444; 455; 462; 468; 481; 495; 518; 540; 546; 555; 572; 585; 594; 630; 660; 666; 693; 702; 715; 740; 756; 770; 777; 780; 814; 819; 858; 910; 924; 945; 962; 990; 999; 1,001; 1,036; 1,092; 1,110; 1,155; 1,170; 1,188; 1,221; 1,260; 1,287; 1,295; 1,332; 1,365; 1,386; 1,404; 1,430; 1,443; 1,485; 1,540; 1,554; 1,628; 1,638; 1,665; 1,716; 1,755; 1,820; 1,890; 1,924; 1,980; 1,998; 2,002; 2,035; 2,079; 2,145; 2,220; 2,310; 2,331; 2,340; 2,405; 2,442; 2,457; 2,574; 2,590; 2,730; 2,772; 2,849; 2,860; 2,886; 2,970; 3,003; 3,108; 3,276; 3,330; 3,367; 3,465; 3,510; 3,663; 3,780; 3,861; 3,885; 3,996; 4,004; 4,070; 4,095; 4,158; 4,290; 4,329; 4,620; 4,662; 4,810; 4,884; 4,914; 4,995; 5,005; 5,148; 5,180; 5,291; 5,460; 5,698; 5,772; 5,940; 6,006; 6,105; 6,435; 6,660; 6,734; 6,930; 6,993; 7,020; 7,215; 7,326; 7,722; 7,770; 8,140; 8,190; 8,316; 8,547; 8,580; 8,658; 9,009; 9,324; 9,620; 9,828; 9,990; 10,010; 10,101; 10,395; 10,582; 10,989; 11,396; 11,655; 12,012; 12,210; 12,285; 12,870; 12,987; 13,468; 13,860; 13,986; 14,245; 14,430; 14,652; 15,015; 15,444; 15,540; 15,873; 16,380; 16,835; 17,094; 17,316; 18,018; 18,315; 19,305; 19,980; 20,020; 20,202; 20,790; 21,164; 21,645; 21,978; 23,310; 24,420; 24,570; 25,641; 25,740; 25,974; 26,455; 27,027; 27,972; 28,490; 28,860; 30,030; 30,303; 31,746; 33,670; 34,188; 34,965; 36,036; 36,630; 37,037; 38,610; 40,404; 41,580; 42,735; 43,290; 43,956; 45,045; 46,620; 47,619; 49,140; 50,505; 51,282; 51,948; 52,910; 54,054; 54,945; 56,980; 60,060; 60,606; 63,492; 64,935; 67,340; 69,930; 73,260; 74,074; 76,923; 77,220; 79,365; 85,470; 86,580; 90,090; 90,909; 95,238; 101,010; 102,564; 105,820; 108,108; 109,890; 111,111; 121,212; 128,205; 129,870; 135,135; 139,860; 142,857; 148,148; 151,515; 153,846; 158,730; 170,940; 180,180; 181,818; 185,185; 190,476; 202,020; 219,780; 222,222; 238,095; 256,410; 259,740; 270,270; 285,714; 303,030; 307,692; 317,460; 333,333; 363,636; 370,370; 384,615; 444,444; 454,545; 476,190; 512,820; 540,540; 555,555; 571,428; 606,060; 666,666; 714,285; 740,740; 769,230; 909,090; 952,380; 999,999; 1,111,110; 1,333,332; 1,428,570; 1,538,460; 1,666,665; 1,818,180; 1,999,998; 2,222,220; 2,857,140; 3,333,330; 3,999,996; 4,999,995; 6,666,660; 9,999,990 and 19,999,980
out of which 7 prime factors: 2; 3; 5; 7; 11; 13 and 37
19,999,980 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.


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".