Given the Number 30,663,360, Calculate (Find) All the Factors (All the Divisors) of the Number 30,663,360 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 30,663,360

1. Carry out the prime factorization of the number 30,663,360:

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

30,663,360 = 26 × 34 × 5 × 7 × 132
30,663,360 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 30,663,360

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
32 = 9
2 × 5 = 10
22 × 3 = 12
prime factor = 13
2 × 7 = 14
3 × 5 = 15
24 = 16
2 × 32 = 18
22 × 5 = 20
3 × 7 = 21
23 × 3 = 24
2 × 13 = 26
33 = 27
22 × 7 = 28
2 × 3 × 5 = 30
25 = 32
5 × 7 = 35
22 × 32 = 36
3 × 13 = 39
23 × 5 = 40
2 × 3 × 7 = 42
32 × 5 = 45
24 × 3 = 48
22 × 13 = 52
2 × 33 = 54
23 × 7 = 56
22 × 3 × 5 = 60
32 × 7 = 63
26 = 64
5 × 13 = 65
2 × 5 × 7 = 70
23 × 32 = 72
2 × 3 × 13 = 78
24 × 5 = 80
34 = 81
22 × 3 × 7 = 84
2 × 32 × 5 = 90
7 × 13 = 91
25 × 3 = 96
23 × 13 = 104
3 × 5 × 7 = 105
22 × 33 = 108
24 × 7 = 112
32 × 13 = 117
23 × 3 × 5 = 120
2 × 32 × 7 = 126
2 × 5 × 13 = 130
33 × 5 = 135
22 × 5 × 7 = 140
24 × 32 = 144
22 × 3 × 13 = 156
25 × 5 = 160
2 × 34 = 162
23 × 3 × 7 = 168
132 = 169
22 × 32 × 5 = 180
2 × 7 × 13 = 182
33 × 7 = 189
26 × 3 = 192
3 × 5 × 13 = 195
24 × 13 = 208
2 × 3 × 5 × 7 = 210
23 × 33 = 216
25 × 7 = 224
2 × 32 × 13 = 234
24 × 3 × 5 = 240
22 × 32 × 7 = 252
22 × 5 × 13 = 260
2 × 33 × 5 = 270
3 × 7 × 13 = 273
23 × 5 × 7 = 280
25 × 32 = 288
23 × 3 × 13 = 312
32 × 5 × 7 = 315
26 × 5 = 320
22 × 34 = 324
24 × 3 × 7 = 336
2 × 132 = 338
33 × 13 = 351
23 × 32 × 5 = 360
22 × 7 × 13 = 364
2 × 33 × 7 = 378
2 × 3 × 5 × 13 = 390
34 × 5 = 405
25 × 13 = 416
22 × 3 × 5 × 7 = 420
24 × 33 = 432
26 × 7 = 448
5 × 7 × 13 = 455
22 × 32 × 13 = 468
25 × 3 × 5 = 480
23 × 32 × 7 = 504
3 × 132 = 507
23 × 5 × 13 = 520
22 × 33 × 5 = 540
2 × 3 × 7 × 13 = 546
24 × 5 × 7 = 560
34 × 7 = 567
26 × 32 = 576
32 × 5 × 13 = 585
24 × 3 × 13 = 624
2 × 32 × 5 × 7 = 630
23 × 34 = 648
25 × 3 × 7 = 672
22 × 132 = 676
2 × 33 × 13 = 702
24 × 32 × 5 = 720
23 × 7 × 13 = 728
22 × 33 × 7 = 756
22 × 3 × 5 × 13 = 780
2 × 34 × 5 = 810
32 × 7 × 13 = 819
26 × 13 = 832
23 × 3 × 5 × 7 = 840
5 × 132 = 845
25 × 33 = 864
2 × 5 × 7 × 13 = 910
23 × 32 × 13 = 936
33 × 5 × 7 = 945
26 × 3 × 5 = 960
24 × 32 × 7 = 1,008
2 × 3 × 132 = 1,014
24 × 5 × 13 = 1,040
34 × 13 = 1,053
23 × 33 × 5 = 1,080
22 × 3 × 7 × 13 = 1,092
25 × 5 × 7 = 1,120
2 × 34 × 7 = 1,134
2 × 32 × 5 × 13 = 1,170
7 × 132 = 1,183
25 × 3 × 13 = 1,248
22 × 32 × 5 × 7 = 1,260
24 × 34 = 1,296
26 × 3 × 7 = 1,344
23 × 132 = 1,352
3 × 5 × 7 × 13 = 1,365
22 × 33 × 13 = 1,404
25 × 32 × 5 = 1,440
24 × 7 × 13 = 1,456
23 × 33 × 7 = 1,512
32 × 132 = 1,521
23 × 3 × 5 × 13 = 1,560
22 × 34 × 5 = 1,620
2 × 32 × 7 × 13 = 1,638
24 × 3 × 5 × 7 = 1,680
2 × 5 × 132 = 1,690
26 × 33 = 1,728
33 × 5 × 13 = 1,755
22 × 5 × 7 × 13 = 1,820
24 × 32 × 13 = 1,872
2 × 33 × 5 × 7 = 1,890
25 × 32 × 7 = 2,016
22 × 3 × 132 = 2,028
25 × 5 × 13 = 2,080
2 × 34 × 13 = 2,106
24 × 33 × 5 = 2,160
23 × 3 × 7 × 13 = 2,184
26 × 5 × 7 = 2,240
22 × 34 × 7 = 2,268
22 × 32 × 5 × 13 = 2,340
2 × 7 × 132 = 2,366
33 × 7 × 13 = 2,457
26 × 3 × 13 = 2,496
23 × 32 × 5 × 7 = 2,520
3 × 5 × 132 = 2,535
25 × 34 = 2,592
24 × 132 = 2,704
2 × 3 × 5 × 7 × 13 = 2,730
23 × 33 × 13 = 2,808
34 × 5 × 7 = 2,835
26 × 32 × 5 = 2,880
25 × 7 × 13 = 2,912
24 × 33 × 7 = 3,024
2 × 32 × 132 = 3,042
24 × 3 × 5 × 13 = 3,120
23 × 34 × 5 = 3,240
22 × 32 × 7 × 13 = 3,276
25 × 3 × 5 × 7 = 3,360
22 × 5 × 132 = 3,380
2 × 33 × 5 × 13 = 3,510
3 × 7 × 132 = 3,549
23 × 5 × 7 × 13 = 3,640
25 × 32 × 13 = 3,744
22 × 33 × 5 × 7 = 3,780
26 × 32 × 7 = 4,032
23 × 3 × 132 = 4,056
32 × 5 × 7 × 13 = 4,095
26 × 5 × 13 = 4,160
22 × 34 × 13 = 4,212
25 × 33 × 5 = 4,320
24 × 3 × 7 × 13 = 4,368
23 × 34 × 7 = 4,536
33 × 132 = 4,563
23 × 32 × 5 × 13 = 4,680
22 × 7 × 132 = 4,732
2 × 33 × 7 × 13 = 4,914
24 × 32 × 5 × 7 = 5,040
2 × 3 × 5 × 132 = 5,070
26 × 34 = 5,184
34 × 5 × 13 = 5,265
25 × 132 = 5,408
22 × 3 × 5 × 7 × 13 = 5,460
This list continues below...

... This list continues from above
24 × 33 × 13 = 5,616
2 × 34 × 5 × 7 = 5,670
26 × 7 × 13 = 5,824
5 × 7 × 132 = 5,915
25 × 33 × 7 = 6,048
22 × 32 × 132 = 6,084
25 × 3 × 5 × 13 = 6,240
24 × 34 × 5 = 6,480
23 × 32 × 7 × 13 = 6,552
26 × 3 × 5 × 7 = 6,720
23 × 5 × 132 = 6,760
22 × 33 × 5 × 13 = 7,020
2 × 3 × 7 × 132 = 7,098
24 × 5 × 7 × 13 = 7,280
34 × 7 × 13 = 7,371
26 × 32 × 13 = 7,488
23 × 33 × 5 × 7 = 7,560
32 × 5 × 132 = 7,605
24 × 3 × 132 = 8,112
2 × 32 × 5 × 7 × 13 = 8,190
23 × 34 × 13 = 8,424
26 × 33 × 5 = 8,640
25 × 3 × 7 × 13 = 8,736
24 × 34 × 7 = 9,072
2 × 33 × 132 = 9,126
24 × 32 × 5 × 13 = 9,360
23 × 7 × 132 = 9,464
22 × 33 × 7 × 13 = 9,828
25 × 32 × 5 × 7 = 10,080
22 × 3 × 5 × 132 = 10,140
2 × 34 × 5 × 13 = 10,530
32 × 7 × 132 = 10,647
26 × 132 = 10,816
23 × 3 × 5 × 7 × 13 = 10,920
25 × 33 × 13 = 11,232
22 × 34 × 5 × 7 = 11,340
2 × 5 × 7 × 132 = 11,830
26 × 33 × 7 = 12,096
23 × 32 × 132 = 12,168
33 × 5 × 7 × 13 = 12,285
26 × 3 × 5 × 13 = 12,480
25 × 34 × 5 = 12,960
24 × 32 × 7 × 13 = 13,104
24 × 5 × 132 = 13,520
34 × 132 = 13,689
23 × 33 × 5 × 13 = 14,040
22 × 3 × 7 × 132 = 14,196
25 × 5 × 7 × 13 = 14,560
2 × 34 × 7 × 13 = 14,742
24 × 33 × 5 × 7 = 15,120
2 × 32 × 5 × 132 = 15,210
25 × 3 × 132 = 16,224
22 × 32 × 5 × 7 × 13 = 16,380
24 × 34 × 13 = 16,848
26 × 3 × 7 × 13 = 17,472
3 × 5 × 7 × 132 = 17,745
25 × 34 × 7 = 18,144
22 × 33 × 132 = 18,252
25 × 32 × 5 × 13 = 18,720
24 × 7 × 132 = 18,928
23 × 33 × 7 × 13 = 19,656
26 × 32 × 5 × 7 = 20,160
23 × 3 × 5 × 132 = 20,280
22 × 34 × 5 × 13 = 21,060
2 × 32 × 7 × 132 = 21,294
24 × 3 × 5 × 7 × 13 = 21,840
26 × 33 × 13 = 22,464
23 × 34 × 5 × 7 = 22,680
33 × 5 × 132 = 22,815
22 × 5 × 7 × 132 = 23,660
24 × 32 × 132 = 24,336
2 × 33 × 5 × 7 × 13 = 24,570
26 × 34 × 5 = 25,920
25 × 32 × 7 × 13 = 26,208
25 × 5 × 132 = 27,040
2 × 34 × 132 = 27,378
24 × 33 × 5 × 13 = 28,080
23 × 3 × 7 × 132 = 28,392
26 × 5 × 7 × 13 = 29,120
22 × 34 × 7 × 13 = 29,484
25 × 33 × 5 × 7 = 30,240
22 × 32 × 5 × 132 = 30,420
33 × 7 × 132 = 31,941
26 × 3 × 132 = 32,448
23 × 32 × 5 × 7 × 13 = 32,760
25 × 34 × 13 = 33,696
2 × 3 × 5 × 7 × 132 = 35,490
26 × 34 × 7 = 36,288
23 × 33 × 132 = 36,504
34 × 5 × 7 × 13 = 36,855
26 × 32 × 5 × 13 = 37,440
25 × 7 × 132 = 37,856
24 × 33 × 7 × 13 = 39,312
24 × 3 × 5 × 132 = 40,560
23 × 34 × 5 × 13 = 42,120
22 × 32 × 7 × 132 = 42,588
25 × 3 × 5 × 7 × 13 = 43,680
24 × 34 × 5 × 7 = 45,360
2 × 33 × 5 × 132 = 45,630
23 × 5 × 7 × 132 = 47,320
25 × 32 × 132 = 48,672
22 × 33 × 5 × 7 × 13 = 49,140
26 × 32 × 7 × 13 = 52,416
32 × 5 × 7 × 132 = 53,235
26 × 5 × 132 = 54,080
22 × 34 × 132 = 54,756
25 × 33 × 5 × 13 = 56,160
24 × 3 × 7 × 132 = 56,784
23 × 34 × 7 × 13 = 58,968
26 × 33 × 5 × 7 = 60,480
23 × 32 × 5 × 132 = 60,840
2 × 33 × 7 × 132 = 63,882
24 × 32 × 5 × 7 × 13 = 65,520
26 × 34 × 13 = 67,392
34 × 5 × 132 = 68,445
22 × 3 × 5 × 7 × 132 = 70,980
24 × 33 × 132 = 73,008
2 × 34 × 5 × 7 × 13 = 73,710
26 × 7 × 132 = 75,712
25 × 33 × 7 × 13 = 78,624
25 × 3 × 5 × 132 = 81,120
24 × 34 × 5 × 13 = 84,240
23 × 32 × 7 × 132 = 85,176
26 × 3 × 5 × 7 × 13 = 87,360
25 × 34 × 5 × 7 = 90,720
22 × 33 × 5 × 132 = 91,260
24 × 5 × 7 × 132 = 94,640
34 × 7 × 132 = 95,823
26 × 32 × 132 = 97,344
23 × 33 × 5 × 7 × 13 = 98,280
2 × 32 × 5 × 7 × 132 = 106,470
23 × 34 × 132 = 109,512
26 × 33 × 5 × 13 = 112,320
25 × 3 × 7 × 132 = 113,568
24 × 34 × 7 × 13 = 117,936
24 × 32 × 5 × 132 = 121,680
22 × 33 × 7 × 132 = 127,764
25 × 32 × 5 × 7 × 13 = 131,040
2 × 34 × 5 × 132 = 136,890
23 × 3 × 5 × 7 × 132 = 141,960
25 × 33 × 132 = 146,016
22 × 34 × 5 × 7 × 13 = 147,420
26 × 33 × 7 × 13 = 157,248
33 × 5 × 7 × 132 = 159,705
26 × 3 × 5 × 132 = 162,240
25 × 34 × 5 × 13 = 168,480
24 × 32 × 7 × 132 = 170,352
26 × 34 × 5 × 7 = 181,440
23 × 33 × 5 × 132 = 182,520
25 × 5 × 7 × 132 = 189,280
2 × 34 × 7 × 132 = 191,646
24 × 33 × 5 × 7 × 13 = 196,560
22 × 32 × 5 × 7 × 132 = 212,940
24 × 34 × 132 = 219,024
26 × 3 × 7 × 132 = 227,136
25 × 34 × 7 × 13 = 235,872
25 × 32 × 5 × 132 = 243,360
23 × 33 × 7 × 132 = 255,528
26 × 32 × 5 × 7 × 13 = 262,080
22 × 34 × 5 × 132 = 273,780
24 × 3 × 5 × 7 × 132 = 283,920
26 × 33 × 132 = 292,032
23 × 34 × 5 × 7 × 13 = 294,840
2 × 33 × 5 × 7 × 132 = 319,410
26 × 34 × 5 × 13 = 336,960
25 × 32 × 7 × 132 = 340,704
24 × 33 × 5 × 132 = 365,040
26 × 5 × 7 × 132 = 378,560
22 × 34 × 7 × 132 = 383,292
25 × 33 × 5 × 7 × 13 = 393,120
23 × 32 × 5 × 7 × 132 = 425,880
25 × 34 × 132 = 438,048
26 × 34 × 7 × 13 = 471,744
34 × 5 × 7 × 132 = 479,115
26 × 32 × 5 × 132 = 486,720
24 × 33 × 7 × 132 = 511,056
23 × 34 × 5 × 132 = 547,560
25 × 3 × 5 × 7 × 132 = 567,840
24 × 34 × 5 × 7 × 13 = 589,680
22 × 33 × 5 × 7 × 132 = 638,820
26 × 32 × 7 × 132 = 681,408
25 × 33 × 5 × 132 = 730,080
23 × 34 × 7 × 132 = 766,584
26 × 33 × 5 × 7 × 13 = 786,240
24 × 32 × 5 × 7 × 132 = 851,760
26 × 34 × 132 = 876,096
2 × 34 × 5 × 7 × 132 = 958,230
25 × 33 × 7 × 132 = 1,022,112
24 × 34 × 5 × 132 = 1,095,120
26 × 3 × 5 × 7 × 132 = 1,135,680
25 × 34 × 5 × 7 × 13 = 1,179,360
23 × 33 × 5 × 7 × 132 = 1,277,640
26 × 33 × 5 × 132 = 1,460,160
24 × 34 × 7 × 132 = 1,533,168
25 × 32 × 5 × 7 × 132 = 1,703,520
22 × 34 × 5 × 7 × 132 = 1,916,460
26 × 33 × 7 × 132 = 2,044,224
25 × 34 × 5 × 132 = 2,190,240
26 × 34 × 5 × 7 × 13 = 2,358,720
24 × 33 × 5 × 7 × 132 = 2,555,280
25 × 34 × 7 × 132 = 3,066,336
26 × 32 × 5 × 7 × 132 = 3,407,040
23 × 34 × 5 × 7 × 132 = 3,832,920
26 × 34 × 5 × 132 = 4,380,480
25 × 33 × 5 × 7 × 132 = 5,110,560
26 × 34 × 7 × 132 = 6,132,672
24 × 34 × 5 × 7 × 132 = 7,665,840
26 × 33 × 5 × 7 × 132 = 10,221,120
25 × 34 × 5 × 7 × 132 = 15,331,680
26 × 34 × 5 × 7 × 132 = 30,663,360

The final answer:
(scroll down)

30,663,360 has 420 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 12; 13; 14; 15; 16; 18; 20; 21; 24; 26; 27; 28; 30; 32; 35; 36; 39; 40; 42; 45; 48; 52; 54; 56; 60; 63; 64; 65; 70; 72; 78; 80; 81; 84; 90; 91; 96; 104; 105; 108; 112; 117; 120; 126; 130; 135; 140; 144; 156; 160; 162; 168; 169; 180; 182; 189; 192; 195; 208; 210; 216; 224; 234; 240; 252; 260; 270; 273; 280; 288; 312; 315; 320; 324; 336; 338; 351; 360; 364; 378; 390; 405; 416; 420; 432; 448; 455; 468; 480; 504; 507; 520; 540; 546; 560; 567; 576; 585; 624; 630; 648; 672; 676; 702; 720; 728; 756; 780; 810; 819; 832; 840; 845; 864; 910; 936; 945; 960; 1,008; 1,014; 1,040; 1,053; 1,080; 1,092; 1,120; 1,134; 1,170; 1,183; 1,248; 1,260; 1,296; 1,344; 1,352; 1,365; 1,404; 1,440; 1,456; 1,512; 1,521; 1,560; 1,620; 1,638; 1,680; 1,690; 1,728; 1,755; 1,820; 1,872; 1,890; 2,016; 2,028; 2,080; 2,106; 2,160; 2,184; 2,240; 2,268; 2,340; 2,366; 2,457; 2,496; 2,520; 2,535; 2,592; 2,704; 2,730; 2,808; 2,835; 2,880; 2,912; 3,024; 3,042; 3,120; 3,240; 3,276; 3,360; 3,380; 3,510; 3,549; 3,640; 3,744; 3,780; 4,032; 4,056; 4,095; 4,160; 4,212; 4,320; 4,368; 4,536; 4,563; 4,680; 4,732; 4,914; 5,040; 5,070; 5,184; 5,265; 5,408; 5,460; 5,616; 5,670; 5,824; 5,915; 6,048; 6,084; 6,240; 6,480; 6,552; 6,720; 6,760; 7,020; 7,098; 7,280; 7,371; 7,488; 7,560; 7,605; 8,112; 8,190; 8,424; 8,640; 8,736; 9,072; 9,126; 9,360; 9,464; 9,828; 10,080; 10,140; 10,530; 10,647; 10,816; 10,920; 11,232; 11,340; 11,830; 12,096; 12,168; 12,285; 12,480; 12,960; 13,104; 13,520; 13,689; 14,040; 14,196; 14,560; 14,742; 15,120; 15,210; 16,224; 16,380; 16,848; 17,472; 17,745; 18,144; 18,252; 18,720; 18,928; 19,656; 20,160; 20,280; 21,060; 21,294; 21,840; 22,464; 22,680; 22,815; 23,660; 24,336; 24,570; 25,920; 26,208; 27,040; 27,378; 28,080; 28,392; 29,120; 29,484; 30,240; 30,420; 31,941; 32,448; 32,760; 33,696; 35,490; 36,288; 36,504; 36,855; 37,440; 37,856; 39,312; 40,560; 42,120; 42,588; 43,680; 45,360; 45,630; 47,320; 48,672; 49,140; 52,416; 53,235; 54,080; 54,756; 56,160; 56,784; 58,968; 60,480; 60,840; 63,882; 65,520; 67,392; 68,445; 70,980; 73,008; 73,710; 75,712; 78,624; 81,120; 84,240; 85,176; 87,360; 90,720; 91,260; 94,640; 95,823; 97,344; 98,280; 106,470; 109,512; 112,320; 113,568; 117,936; 121,680; 127,764; 131,040; 136,890; 141,960; 146,016; 147,420; 157,248; 159,705; 162,240; 168,480; 170,352; 181,440; 182,520; 189,280; 191,646; 196,560; 212,940; 219,024; 227,136; 235,872; 243,360; 255,528; 262,080; 273,780; 283,920; 292,032; 294,840; 319,410; 336,960; 340,704; 365,040; 378,560; 383,292; 393,120; 425,880; 438,048; 471,744; 479,115; 486,720; 511,056; 547,560; 567,840; 589,680; 638,820; 681,408; 730,080; 766,584; 786,240; 851,760; 876,096; 958,230; 1,022,112; 1,095,120; 1,135,680; 1,179,360; 1,277,640; 1,460,160; 1,533,168; 1,703,520; 1,916,460; 2,044,224; 2,190,240; 2,358,720; 2,555,280; 3,066,336; 3,407,040; 3,832,920; 4,380,480; 5,110,560; 6,132,672; 7,665,840; 10,221,120; 15,331,680 and 30,663,360
out of which 5 prime factors: 2; 3; 5; 7 and 13
30,663,360 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 30,663,347?

» What are all the proper, improper and prime factors (divisors) of the number 30,663,374?


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".