Given the Number 89,999,910 Calculate (Find) All Its Factors (Divisors – the Proper, the Improper and the Prime Factors). Online Calculator

All the factors (divisors) of the number 89,999,910

1. Carry out the prime factorization of the number 89,999,910:

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


89,999,910 = 2 × 35 × 5 × 7 × 11 × 13 × 37
89,999,910 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 89,999,910

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
prime factor = 5
2 × 3 = 6
prime factor = 7
32 = 9
2 × 5 = 10
prime factor = 11
prime factor = 13
2 × 7 = 14
3 × 5 = 15
2 × 32 = 18
3 × 7 = 21
2 × 11 = 22
2 × 13 = 26
33 = 27
2 × 3 × 5 = 30
3 × 11 = 33
5 × 7 = 35
prime factor = 37
3 × 13 = 39
2 × 3 × 7 = 42
32 × 5 = 45
2 × 33 = 54
5 × 11 = 55
32 × 7 = 63
5 × 13 = 65
2 × 3 × 11 = 66
2 × 5 × 7 = 70
2 × 37 = 74
7 × 11 = 77
2 × 3 × 13 = 78
34 = 81
2 × 32 × 5 = 90
7 × 13 = 91
32 × 11 = 99
3 × 5 × 7 = 105
2 × 5 × 11 = 110
3 × 37 = 111
32 × 13 = 117
2 × 32 × 7 = 126
2 × 5 × 13 = 130
33 × 5 = 135
11 × 13 = 143
2 × 7 × 11 = 154
2 × 34 = 162
3 × 5 × 11 = 165
2 × 7 × 13 = 182
5 × 37 = 185
33 × 7 = 189
3 × 5 × 13 = 195
2 × 32 × 11 = 198
2 × 3 × 5 × 7 = 210
2 × 3 × 37 = 222
3 × 7 × 11 = 231
2 × 32 × 13 = 234
35 = 243
7 × 37 = 259
2 × 33 × 5 = 270
3 × 7 × 13 = 273
2 × 11 × 13 = 286
33 × 11 = 297
32 × 5 × 7 = 315
2 × 3 × 5 × 11 = 330
32 × 37 = 333
33 × 13 = 351
2 × 5 × 37 = 370
2 × 33 × 7 = 378
5 × 7 × 11 = 385
2 × 3 × 5 × 13 = 390
34 × 5 = 405
11 × 37 = 407
3 × 11 × 13 = 429
5 × 7 × 13 = 455
2 × 3 × 7 × 11 = 462
13 × 37 = 481
2 × 35 = 486
32 × 5 × 11 = 495
2 × 7 × 37 = 518
2 × 3 × 7 × 13 = 546
3 × 5 × 37 = 555
34 × 7 = 567
32 × 5 × 13 = 585
2 × 33 × 11 = 594
2 × 32 × 5 × 7 = 630
2 × 32 × 37 = 666
32 × 7 × 11 = 693
2 × 33 × 13 = 702
5 × 11 × 13 = 715
2 × 5 × 7 × 11 = 770
3 × 7 × 37 = 777
2 × 34 × 5 = 810
2 × 11 × 37 = 814
32 × 7 × 13 = 819
2 × 3 × 11 × 13 = 858
34 × 11 = 891
2 × 5 × 7 × 13 = 910
33 × 5 × 7 = 945
2 × 13 × 37 = 962
2 × 32 × 5 × 11 = 990
33 × 37 = 999
7 × 11 × 13 = 1,001
34 × 13 = 1,053
2 × 3 × 5 × 37 = 1,110
2 × 34 × 7 = 1,134
3 × 5 × 7 × 11 = 1,155
2 × 32 × 5 × 13 = 1,170
35 × 5 = 1,215
3 × 11 × 37 = 1,221
32 × 11 × 13 = 1,287
5 × 7 × 37 = 1,295
3 × 5 × 7 × 13 = 1,365
2 × 32 × 7 × 11 = 1,386
2 × 5 × 11 × 13 = 1,430
3 × 13 × 37 = 1,443
33 × 5 × 11 = 1,485
2 × 3 × 7 × 37 = 1,554
2 × 32 × 7 × 13 = 1,638
32 × 5 × 37 = 1,665
35 × 7 = 1,701
33 × 5 × 13 = 1,755
2 × 34 × 11 = 1,782
2 × 33 × 5 × 7 = 1,890
2 × 33 × 37 = 1,998
2 × 7 × 11 × 13 = 2,002
5 × 11 × 37 = 2,035
33 × 7 × 11 = 2,079
2 × 34 × 13 = 2,106
3 × 5 × 11 × 13 = 2,145
2 × 3 × 5 × 7 × 11 = 2,310
32 × 7 × 37 = 2,331
5 × 13 × 37 = 2,405
2 × 35 × 5 = 2,430
2 × 3 × 11 × 37 = 2,442
33 × 7 × 13 = 2,457
2 × 32 × 11 × 13 = 2,574
2 × 5 × 7 × 37 = 2,590
35 × 11 = 2,673
2 × 3 × 5 × 7 × 13 = 2,730
34 × 5 × 7 = 2,835
7 × 11 × 37 = 2,849
2 × 3 × 13 × 37 = 2,886
2 × 33 × 5 × 11 = 2,970
34 × 37 = 2,997
3 × 7 × 11 × 13 = 3,003
35 × 13 = 3,159
2 × 32 × 5 × 37 = 3,330
7 × 13 × 37 = 3,367
2 × 35 × 7 = 3,402
32 × 5 × 7 × 11 = 3,465
2 × 33 × 5 × 13 = 3,510
32 × 11 × 37 = 3,663
33 × 11 × 13 = 3,861
3 × 5 × 7 × 37 = 3,885
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
34 × 5 × 11 = 4,455
2 × 32 × 7 × 37 = 4,662
2 × 5 × 13 × 37 = 4,810
2 × 33 × 7 × 13 = 4,914
33 × 5 × 37 = 4,995
5 × 7 × 11 × 13 = 5,005
34 × 5 × 13 = 5,265
11 × 13 × 37 = 5,291
2 × 35 × 11 = 5,346
2 × 34 × 5 × 7 = 5,670
2 × 7 × 11 × 37 = 5,698
2 × 34 × 37 = 5,994
2 × 3 × 7 × 11 × 13 = 6,006
3 × 5 × 11 × 37 = 6,105
34 × 7 × 11 = 6,237
2 × 35 × 13 = 6,318
32 × 5 × 11 × 13 = 6,435
2 × 7 × 13 × 37 = 6,734
2 × 32 × 5 × 7 × 11 = 6,930
33 × 7 × 37 = 6,993
3 × 5 × 13 × 37 = 7,215
2 × 32 × 11 × 37 = 7,326
34 × 7 × 13 = 7,371
2 × 33 × 11 × 13 = 7,722
2 × 3 × 5 × 7 × 37 = 7,770
2 × 32 × 5 × 7 × 13 = 8,190
35 × 5 × 7 = 8,505
3 × 7 × 11 × 37 = 8,547
2 × 32 × 13 × 37 = 8,658
2 × 34 × 5 × 11 = 8,910
35 × 37 = 8,991
32 × 7 × 11 × 13 = 9,009
This list continues below...

... This list continues from above
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 × 34 × 5 × 13 = 10,530
2 × 11 × 13 × 37 = 10,582
33 × 11 × 37 = 10,989
34 × 11 × 13 = 11,583
32 × 5 × 7 × 37 = 11,655
2 × 3 × 5 × 11 × 37 = 12,210
33 × 5 × 7 × 13 = 12,285
2 × 34 × 7 × 11 = 12,474
2 × 32 × 5 × 11 × 13 = 12,870
33 × 13 × 37 = 12,987
35 × 5 × 11 = 13,365
2 × 33 × 7 × 37 = 13,986
5 × 7 × 11 × 37 = 14,245
2 × 3 × 5 × 13 × 37 = 14,430
2 × 34 × 7 × 13 = 14,742
34 × 5 × 37 = 14,985
3 × 5 × 7 × 11 × 13 = 15,015
35 × 5 × 13 = 15,795
3 × 11 × 13 × 37 = 15,873
5 × 7 × 13 × 37 = 16,835
2 × 35 × 5 × 7 = 17,010
2 × 3 × 7 × 11 × 37 = 17,094
2 × 35 × 37 = 17,982
2 × 32 × 7 × 11 × 13 = 18,018
32 × 5 × 11 × 37 = 18,315
35 × 7 × 11 = 18,711
33 × 5 × 11 × 13 = 19,305
2 × 3 × 7 × 13 × 37 = 20,202
2 × 33 × 5 × 7 × 11 = 20,790
34 × 7 × 37 = 20,979
32 × 5 × 13 × 37 = 21,645
2 × 33 × 11 × 37 = 21,978
35 × 7 × 13 = 22,113
2 × 34 × 11 × 13 = 23,166
2 × 32 × 5 × 7 × 37 = 23,310
2 × 33 × 5 × 7 × 13 = 24,570
32 × 7 × 11 × 37 = 25,641
2 × 33 × 13 × 37 = 25,974
5 × 11 × 13 × 37 = 26,455
2 × 35 × 5 × 11 = 26,730
33 × 7 × 11 × 13 = 27,027
2 × 5 × 7 × 11 × 37 = 28,490
2 × 34 × 5 × 37 = 29,970
2 × 3 × 5 × 7 × 11 × 13 = 30,030
32 × 7 × 13 × 37 = 30,303
34 × 5 × 7 × 11 = 31,185
2 × 35 × 5 × 13 = 31,590
2 × 3 × 11 × 13 × 37 = 31,746
34 × 11 × 37 = 32,967
2 × 5 × 7 × 13 × 37 = 33,670
35 × 11 × 13 = 34,749
33 × 5 × 7 × 37 = 34,965
2 × 32 × 5 × 11 × 37 = 36,630
34 × 5 × 7 × 13 = 36,855
7 × 11 × 13 × 37 = 37,037
2 × 35 × 7 × 11 = 37,422
2 × 33 × 5 × 11 × 13 = 38,610
34 × 13 × 37 = 38,961
2 × 34 × 7 × 37 = 41,958
3 × 5 × 7 × 11 × 37 = 42,735
2 × 32 × 5 × 13 × 37 = 43,290
2 × 35 × 7 × 13 = 44,226
35 × 5 × 37 = 44,955
32 × 5 × 7 × 11 × 13 = 45,045
32 × 11 × 13 × 37 = 47,619
3 × 5 × 7 × 13 × 37 = 50,505
2 × 32 × 7 × 11 × 37 = 51,282
2 × 5 × 11 × 13 × 37 = 52,910
2 × 33 × 7 × 11 × 13 = 54,054
33 × 5 × 11 × 37 = 54,945
34 × 5 × 11 × 13 = 57,915
2 × 32 × 7 × 13 × 37 = 60,606
2 × 34 × 5 × 7 × 11 = 62,370
35 × 7 × 37 = 62,937
33 × 5 × 13 × 37 = 64,935
2 × 34 × 11 × 37 = 65,934
2 × 35 × 11 × 13 = 69,498
2 × 33 × 5 × 7 × 37 = 69,930
2 × 34 × 5 × 7 × 13 = 73,710
2 × 7 × 11 × 13 × 37 = 74,074
33 × 7 × 11 × 37 = 76,923
2 × 34 × 13 × 37 = 77,922
3 × 5 × 11 × 13 × 37 = 79,365
34 × 7 × 11 × 13 = 81,081
2 × 3 × 5 × 7 × 11 × 37 = 85,470
2 × 35 × 5 × 37 = 89,910
2 × 32 × 5 × 7 × 11 × 13 = 90,090
33 × 7 × 13 × 37 = 90,909
35 × 5 × 7 × 11 = 93,555
2 × 32 × 11 × 13 × 37 = 95,238
35 × 11 × 37 = 98,901
2 × 3 × 5 × 7 × 13 × 37 = 101,010
34 × 5 × 7 × 37 = 104,895
2 × 33 × 5 × 11 × 37 = 109,890
35 × 5 × 7 × 13 = 110,565
3 × 7 × 11 × 13 × 37 = 111,111
2 × 34 × 5 × 11 × 13 = 115,830
35 × 13 × 37 = 116,883
2 × 35 × 7 × 37 = 125,874
32 × 5 × 7 × 11 × 37 = 128,205
2 × 33 × 5 × 13 × 37 = 129,870
33 × 5 × 7 × 11 × 13 = 135,135
33 × 11 × 13 × 37 = 142,857
32 × 5 × 7 × 13 × 37 = 151,515
2 × 33 × 7 × 11 × 37 = 153,846
2 × 3 × 5 × 11 × 13 × 37 = 158,730
2 × 34 × 7 × 11 × 13 = 162,162
34 × 5 × 11 × 37 = 164,835
35 × 5 × 11 × 13 = 173,745
2 × 33 × 7 × 13 × 37 = 181,818
5 × 7 × 11 × 13 × 37 = 185,185
2 × 35 × 5 × 7 × 11 = 187,110
34 × 5 × 13 × 37 = 194,805
2 × 35 × 11 × 37 = 197,802
2 × 34 × 5 × 7 × 37 = 209,790
2 × 35 × 5 × 7 × 13 = 221,130
2 × 3 × 7 × 11 × 13 × 37 = 222,222
34 × 7 × 11 × 37 = 230,769
2 × 35 × 13 × 37 = 233,766
32 × 5 × 11 × 13 × 37 = 238,095
35 × 7 × 11 × 13 = 243,243
2 × 32 × 5 × 7 × 11 × 37 = 256,410
2 × 33 × 5 × 7 × 11 × 13 = 270,270
34 × 7 × 13 × 37 = 272,727
2 × 33 × 11 × 13 × 37 = 285,714
2 × 32 × 5 × 7 × 13 × 37 = 303,030
35 × 5 × 7 × 37 = 314,685
2 × 34 × 5 × 11 × 37 = 329,670
32 × 7 × 11 × 13 × 37 = 333,333
2 × 35 × 5 × 11 × 13 = 347,490
2 × 5 × 7 × 11 × 13 × 37 = 370,370
33 × 5 × 7 × 11 × 37 = 384,615
2 × 34 × 5 × 13 × 37 = 389,610
34 × 5 × 7 × 11 × 13 = 405,405
34 × 11 × 13 × 37 = 428,571
33 × 5 × 7 × 13 × 37 = 454,545
2 × 34 × 7 × 11 × 37 = 461,538
2 × 32 × 5 × 11 × 13 × 37 = 476,190
2 × 35 × 7 × 11 × 13 = 486,486
35 × 5 × 11 × 37 = 494,505
2 × 34 × 7 × 13 × 37 = 545,454
3 × 5 × 7 × 11 × 13 × 37 = 555,555
35 × 5 × 13 × 37 = 584,415
2 × 35 × 5 × 7 × 37 = 629,370
2 × 32 × 7 × 11 × 13 × 37 = 666,666
35 × 7 × 11 × 37 = 692,307
33 × 5 × 11 × 13 × 37 = 714,285
2 × 33 × 5 × 7 × 11 × 37 = 769,230
2 × 34 × 5 × 7 × 11 × 13 = 810,810
35 × 7 × 13 × 37 = 818,181
2 × 34 × 11 × 13 × 37 = 857,142
2 × 33 × 5 × 7 × 13 × 37 = 909,090
2 × 35 × 5 × 11 × 37 = 989,010
33 × 7 × 11 × 13 × 37 = 999,999
2 × 3 × 5 × 7 × 11 × 13 × 37 = 1,111,110
34 × 5 × 7 × 11 × 37 = 1,153,845
2 × 35 × 5 × 13 × 37 = 1,168,830
35 × 5 × 7 × 11 × 13 = 1,216,215
35 × 11 × 13 × 37 = 1,285,713
34 × 5 × 7 × 13 × 37 = 1,363,635
2 × 35 × 7 × 11 × 37 = 1,384,614
2 × 33 × 5 × 11 × 13 × 37 = 1,428,570
2 × 35 × 7 × 13 × 37 = 1,636,362
32 × 5 × 7 × 11 × 13 × 37 = 1,666,665
2 × 33 × 7 × 11 × 13 × 37 = 1,999,998
34 × 5 × 11 × 13 × 37 = 2,142,855
2 × 34 × 5 × 7 × 11 × 37 = 2,307,690
2 × 35 × 5 × 7 × 11 × 13 = 2,432,430
2 × 35 × 11 × 13 × 37 = 2,571,426
2 × 34 × 5 × 7 × 13 × 37 = 2,727,270
34 × 7 × 11 × 13 × 37 = 2,999,997
2 × 32 × 5 × 7 × 11 × 13 × 37 = 3,333,330
35 × 5 × 7 × 11 × 37 = 3,461,535
35 × 5 × 7 × 13 × 37 = 4,090,905
2 × 34 × 5 × 11 × 13 × 37 = 4,285,710
33 × 5 × 7 × 11 × 13 × 37 = 4,999,995
2 × 34 × 7 × 11 × 13 × 37 = 5,999,994
35 × 5 × 11 × 13 × 37 = 6,428,565
2 × 35 × 5 × 7 × 11 × 37 = 6,923,070
2 × 35 × 5 × 7 × 13 × 37 = 8,181,810
35 × 7 × 11 × 13 × 37 = 8,999,991
2 × 33 × 5 × 7 × 11 × 13 × 37 = 9,999,990
2 × 35 × 5 × 11 × 13 × 37 = 12,857,130
34 × 5 × 7 × 11 × 13 × 37 = 14,999,985
2 × 35 × 7 × 11 × 13 × 37 = 17,999,982
2 × 34 × 5 × 7 × 11 × 13 × 37 = 29,999,970
35 × 5 × 7 × 11 × 13 × 37 = 44,999,955
2 × 35 × 5 × 7 × 11 × 13 × 37 = 89,999,910

The final answer:
(scroll down)

89,999,910 has 384 factors (divisors):
1; 2; 3; 5; 6; 7; 9; 10; 11; 13; 14; 15; 18; 21; 22; 26; 27; 30; 33; 35; 37; 39; 42; 45; 54; 55; 63; 65; 66; 70; 74; 77; 78; 81; 90; 91; 99; 105; 110; 111; 117; 126; 130; 135; 143; 154; 162; 165; 182; 185; 189; 195; 198; 210; 222; 231; 234; 243; 259; 270; 273; 286; 297; 315; 330; 333; 351; 370; 378; 385; 390; 405; 407; 429; 455; 462; 481; 486; 495; 518; 546; 555; 567; 585; 594; 630; 666; 693; 702; 715; 770; 777; 810; 814; 819; 858; 891; 910; 945; 962; 990; 999; 1,001; 1,053; 1,110; 1,134; 1,155; 1,170; 1,215; 1,221; 1,287; 1,295; 1,365; 1,386; 1,430; 1,443; 1,485; 1,554; 1,638; 1,665; 1,701; 1,755; 1,782; 1,890; 1,998; 2,002; 2,035; 2,079; 2,106; 2,145; 2,310; 2,331; 2,405; 2,430; 2,442; 2,457; 2,574; 2,590; 2,673; 2,730; 2,835; 2,849; 2,886; 2,970; 2,997; 3,003; 3,159; 3,330; 3,367; 3,402; 3,465; 3,510; 3,663; 3,861; 3,885; 4,070; 4,095; 4,158; 4,290; 4,329; 4,455; 4,662; 4,810; 4,914; 4,995; 5,005; 5,265; 5,291; 5,346; 5,670; 5,698; 5,994; 6,006; 6,105; 6,237; 6,318; 6,435; 6,734; 6,930; 6,993; 7,215; 7,326; 7,371; 7,722; 7,770; 8,190; 8,505; 8,547; 8,658; 8,910; 8,991; 9,009; 9,990; 10,010; 10,101; 10,395; 10,530; 10,582; 10,989; 11,583; 11,655; 12,210; 12,285; 12,474; 12,870; 12,987; 13,365; 13,986; 14,245; 14,430; 14,742; 14,985; 15,015; 15,795; 15,873; 16,835; 17,010; 17,094; 17,982; 18,018; 18,315; 18,711; 19,305; 20,202; 20,790; 20,979; 21,645; 21,978; 22,113; 23,166; 23,310; 24,570; 25,641; 25,974; 26,455; 26,730; 27,027; 28,490; 29,970; 30,030; 30,303; 31,185; 31,590; 31,746; 32,967; 33,670; 34,749; 34,965; 36,630; 36,855; 37,037; 37,422; 38,610; 38,961; 41,958; 42,735; 43,290; 44,226; 44,955; 45,045; 47,619; 50,505; 51,282; 52,910; 54,054; 54,945; 57,915; 60,606; 62,370; 62,937; 64,935; 65,934; 69,498; 69,930; 73,710; 74,074; 76,923; 77,922; 79,365; 81,081; 85,470; 89,910; 90,090; 90,909; 93,555; 95,238; 98,901; 101,010; 104,895; 109,890; 110,565; 111,111; 115,830; 116,883; 125,874; 128,205; 129,870; 135,135; 142,857; 151,515; 153,846; 158,730; 162,162; 164,835; 173,745; 181,818; 185,185; 187,110; 194,805; 197,802; 209,790; 221,130; 222,222; 230,769; 233,766; 238,095; 243,243; 256,410; 270,270; 272,727; 285,714; 303,030; 314,685; 329,670; 333,333; 347,490; 370,370; 384,615; 389,610; 405,405; 428,571; 454,545; 461,538; 476,190; 486,486; 494,505; 545,454; 555,555; 584,415; 629,370; 666,666; 692,307; 714,285; 769,230; 810,810; 818,181; 857,142; 909,090; 989,010; 999,999; 1,111,110; 1,153,845; 1,168,830; 1,216,215; 1,285,713; 1,363,635; 1,384,614; 1,428,570; 1,636,362; 1,666,665; 1,999,998; 2,142,855; 2,307,690; 2,432,430; 2,571,426; 2,727,270; 2,999,997; 3,333,330; 3,461,535; 4,090,905; 4,285,710; 4,999,995; 5,999,994; 6,428,565; 6,923,070; 8,181,810; 8,999,991; 9,999,990; 12,857,130; 14,999,985; 17,999,982; 29,999,970; 44,999,955 and 89,999,910
out of which 7 prime factors: 2; 3; 5; 7; 11; 13 and 37
89,999,910 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".