Given the Number 558,073,152, Calculate (Find) All the Factors (All the Divisors) of the Number 558,073,152 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 558,073,152

1. Carry out the prime factorization of the number 558,073,152:

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

558,073,152 = 26 × 34 × 72 × 133
558,073,152 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 558,073,152

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
2 × 3 = 6
prime factor = 7
23 = 8
32 = 9
22 × 3 = 12
prime factor = 13
2 × 7 = 14
24 = 16
2 × 32 = 18
3 × 7 = 21
23 × 3 = 24
2 × 13 = 26
33 = 27
22 × 7 = 28
25 = 32
22 × 32 = 36
3 × 13 = 39
2 × 3 × 7 = 42
24 × 3 = 48
72 = 49
22 × 13 = 52
2 × 33 = 54
23 × 7 = 56
32 × 7 = 63
26 = 64
23 × 32 = 72
2 × 3 × 13 = 78
34 = 81
22 × 3 × 7 = 84
7 × 13 = 91
25 × 3 = 96
2 × 72 = 98
23 × 13 = 104
22 × 33 = 108
24 × 7 = 112
32 × 13 = 117
2 × 32 × 7 = 126
24 × 32 = 144
3 × 72 = 147
22 × 3 × 13 = 156
2 × 34 = 162
23 × 3 × 7 = 168
132 = 169
2 × 7 × 13 = 182
33 × 7 = 189
26 × 3 = 192
22 × 72 = 196
24 × 13 = 208
23 × 33 = 216
25 × 7 = 224
2 × 32 × 13 = 234
22 × 32 × 7 = 252
3 × 7 × 13 = 273
25 × 32 = 288
2 × 3 × 72 = 294
23 × 3 × 13 = 312
22 × 34 = 324
24 × 3 × 7 = 336
2 × 132 = 338
33 × 13 = 351
22 × 7 × 13 = 364
2 × 33 × 7 = 378
23 × 72 = 392
25 × 13 = 416
24 × 33 = 432
32 × 72 = 441
26 × 7 = 448
22 × 32 × 13 = 468
23 × 32 × 7 = 504
3 × 132 = 507
2 × 3 × 7 × 13 = 546
34 × 7 = 567
26 × 32 = 576
22 × 3 × 72 = 588
24 × 3 × 13 = 624
72 × 13 = 637
23 × 34 = 648
25 × 3 × 7 = 672
22 × 132 = 676
2 × 33 × 13 = 702
23 × 7 × 13 = 728
22 × 33 × 7 = 756
24 × 72 = 784
32 × 7 × 13 = 819
26 × 13 = 832
25 × 33 = 864
2 × 32 × 72 = 882
23 × 32 × 13 = 936
24 × 32 × 7 = 1,008
2 × 3 × 132 = 1,014
34 × 13 = 1,053
22 × 3 × 7 × 13 = 1,092
2 × 34 × 7 = 1,134
23 × 3 × 72 = 1,176
7 × 132 = 1,183
25 × 3 × 13 = 1,248
2 × 72 × 13 = 1,274
24 × 34 = 1,296
33 × 72 = 1,323
26 × 3 × 7 = 1,344
23 × 132 = 1,352
22 × 33 × 13 = 1,404
24 × 7 × 13 = 1,456
23 × 33 × 7 = 1,512
32 × 132 = 1,521
25 × 72 = 1,568
2 × 32 × 7 × 13 = 1,638
26 × 33 = 1,728
22 × 32 × 72 = 1,764
24 × 32 × 13 = 1,872
3 × 72 × 13 = 1,911
25 × 32 × 7 = 2,016
22 × 3 × 132 = 2,028
2 × 34 × 13 = 2,106
23 × 3 × 7 × 13 = 2,184
133 = 2,197
22 × 34 × 7 = 2,268
24 × 3 × 72 = 2,352
2 × 7 × 132 = 2,366
33 × 7 × 13 = 2,457
26 × 3 × 13 = 2,496
22 × 72 × 13 = 2,548
25 × 34 = 2,592
2 × 33 × 72 = 2,646
24 × 132 = 2,704
23 × 33 × 13 = 2,808
25 × 7 × 13 = 2,912
24 × 33 × 7 = 3,024
2 × 32 × 132 = 3,042
26 × 72 = 3,136
22 × 32 × 7 × 13 = 3,276
23 × 32 × 72 = 3,528
3 × 7 × 132 = 3,549
25 × 32 × 13 = 3,744
2 × 3 × 72 × 13 = 3,822
34 × 72 = 3,969
26 × 32 × 7 = 4,032
23 × 3 × 132 = 4,056
22 × 34 × 13 = 4,212
24 × 3 × 7 × 13 = 4,368
2 × 133 = 4,394
23 × 34 × 7 = 4,536
33 × 132 = 4,563
25 × 3 × 72 = 4,704
22 × 7 × 132 = 4,732
2 × 33 × 7 × 13 = 4,914
23 × 72 × 13 = 5,096
26 × 34 = 5,184
22 × 33 × 72 = 5,292
25 × 132 = 5,408
24 × 33 × 13 = 5,616
32 × 72 × 13 = 5,733
26 × 7 × 13 = 5,824
25 × 33 × 7 = 6,048
22 × 32 × 132 = 6,084
23 × 32 × 7 × 13 = 6,552
3 × 133 = 6,591
24 × 32 × 72 = 7,056
2 × 3 × 7 × 132 = 7,098
34 × 7 × 13 = 7,371
26 × 32 × 13 = 7,488
22 × 3 × 72 × 13 = 7,644
2 × 34 × 72 = 7,938
24 × 3 × 132 = 8,112
72 × 132 = 8,281
23 × 34 × 13 = 8,424
25 × 3 × 7 × 13 = 8,736
22 × 133 = 8,788
24 × 34 × 7 = 9,072
2 × 33 × 132 = 9,126
26 × 3 × 72 = 9,408
23 × 7 × 132 = 9,464
22 × 33 × 7 × 13 = 9,828
24 × 72 × 13 = 10,192
23 × 33 × 72 = 10,584
32 × 7 × 132 = 10,647
26 × 132 = 10,816
25 × 33 × 13 = 11,232
2 × 32 × 72 × 13 = 11,466
26 × 33 × 7 = 12,096
23 × 32 × 132 = 12,168
24 × 32 × 7 × 13 = 13,104
2 × 3 × 133 = 13,182
34 × 132 = 13,689
25 × 32 × 72 = 14,112
22 × 3 × 7 × 132 = 14,196
2 × 34 × 7 × 13 = 14,742
23 × 3 × 72 × 13 = 15,288
7 × 133 = 15,379
22 × 34 × 72 = 15,876
25 × 3 × 132 = 16,224
2 × 72 × 132 = 16,562
24 × 34 × 13 = 16,848
33 × 72 × 13 = 17,199
26 × 3 × 7 × 13 = 17,472
23 × 133 = 17,576
25 × 34 × 7 = 18,144
22 × 33 × 132 = 18,252
24 × 7 × 132 = 18,928
23 × 33 × 7 × 13 = 19,656
32 × 133 = 19,773
25 × 72 × 13 = 20,384
24 × 33 × 72 = 21,168
2 × 32 × 7 × 132 = 21,294
26 × 33 × 13 = 22,464
22 × 32 × 72 × 13 = 22,932
This list continues below...

... This list continues from above
24 × 32 × 132 = 24,336
3 × 72 × 132 = 24,843
25 × 32 × 7 × 13 = 26,208
22 × 3 × 133 = 26,364
2 × 34 × 132 = 27,378
26 × 32 × 72 = 28,224
23 × 3 × 7 × 132 = 28,392
22 × 34 × 7 × 13 = 29,484
24 × 3 × 72 × 13 = 30,576
2 × 7 × 133 = 30,758
23 × 34 × 72 = 31,752
33 × 7 × 132 = 31,941
26 × 3 × 132 = 32,448
22 × 72 × 132 = 33,124
25 × 34 × 13 = 33,696
2 × 33 × 72 × 13 = 34,398
24 × 133 = 35,152
26 × 34 × 7 = 36,288
23 × 33 × 132 = 36,504
25 × 7 × 132 = 37,856
24 × 33 × 7 × 13 = 39,312
2 × 32 × 133 = 39,546
26 × 72 × 13 = 40,768
25 × 33 × 72 = 42,336
22 × 32 × 7 × 132 = 42,588
23 × 32 × 72 × 13 = 45,864
3 × 7 × 133 = 46,137
25 × 32 × 132 = 48,672
2 × 3 × 72 × 132 = 49,686
34 × 72 × 13 = 51,597
26 × 32 × 7 × 13 = 52,416
23 × 3 × 133 = 52,728
22 × 34 × 132 = 54,756
24 × 3 × 7 × 132 = 56,784
23 × 34 × 7 × 13 = 58,968
33 × 133 = 59,319
25 × 3 × 72 × 13 = 61,152
22 × 7 × 133 = 61,516
24 × 34 × 72 = 63,504
2 × 33 × 7 × 132 = 63,882
23 × 72 × 132 = 66,248
26 × 34 × 13 = 67,392
22 × 33 × 72 × 13 = 68,796
25 × 133 = 70,304
24 × 33 × 132 = 73,008
32 × 72 × 132 = 74,529
26 × 7 × 132 = 75,712
25 × 33 × 7 × 13 = 78,624
22 × 32 × 133 = 79,092
26 × 33 × 72 = 84,672
23 × 32 × 7 × 132 = 85,176
24 × 32 × 72 × 13 = 91,728
2 × 3 × 7 × 133 = 92,274
34 × 7 × 132 = 95,823
26 × 32 × 132 = 97,344
22 × 3 × 72 × 132 = 99,372
2 × 34 × 72 × 13 = 103,194
24 × 3 × 133 = 105,456
72 × 133 = 107,653
23 × 34 × 132 = 109,512
25 × 3 × 7 × 132 = 113,568
24 × 34 × 7 × 13 = 117,936
2 × 33 × 133 = 118,638
26 × 3 × 72 × 13 = 122,304
23 × 7 × 133 = 123,032
25 × 34 × 72 = 127,008
22 × 33 × 7 × 132 = 127,764
24 × 72 × 132 = 132,496
23 × 33 × 72 × 13 = 137,592
32 × 7 × 133 = 138,411
26 × 133 = 140,608
25 × 33 × 132 = 146,016
2 × 32 × 72 × 132 = 149,058
26 × 33 × 7 × 13 = 157,248
23 × 32 × 133 = 158,184
24 × 32 × 7 × 132 = 170,352
34 × 133 = 177,957
25 × 32 × 72 × 13 = 183,456
22 × 3 × 7 × 133 = 184,548
2 × 34 × 7 × 132 = 191,646
23 × 3 × 72 × 132 = 198,744
22 × 34 × 72 × 13 = 206,388
25 × 3 × 133 = 210,912
2 × 72 × 133 = 215,306
24 × 34 × 132 = 219,024
33 × 72 × 132 = 223,587
26 × 3 × 7 × 132 = 227,136
25 × 34 × 7 × 13 = 235,872
22 × 33 × 133 = 237,276
24 × 7 × 133 = 246,064
26 × 34 × 72 = 254,016
23 × 33 × 7 × 132 = 255,528
25 × 72 × 132 = 264,992
24 × 33 × 72 × 13 = 275,184
2 × 32 × 7 × 133 = 276,822
26 × 33 × 132 = 292,032
22 × 32 × 72 × 132 = 298,116
24 × 32 × 133 = 316,368
3 × 72 × 133 = 322,959
25 × 32 × 7 × 132 = 340,704
2 × 34 × 133 = 355,914
26 × 32 × 72 × 13 = 366,912
23 × 3 × 7 × 133 = 369,096
22 × 34 × 7 × 132 = 383,292
24 × 3 × 72 × 132 = 397,488
23 × 34 × 72 × 13 = 412,776
33 × 7 × 133 = 415,233
26 × 3 × 133 = 421,824
22 × 72 × 133 = 430,612
25 × 34 × 132 = 438,048
2 × 33 × 72 × 132 = 447,174
26 × 34 × 7 × 13 = 471,744
23 × 33 × 133 = 474,552
25 × 7 × 133 = 492,128
24 × 33 × 7 × 132 = 511,056
26 × 72 × 132 = 529,984
25 × 33 × 72 × 13 = 550,368
22 × 32 × 7 × 133 = 553,644
23 × 32 × 72 × 132 = 596,232
25 × 32 × 133 = 632,736
2 × 3 × 72 × 133 = 645,918
34 × 72 × 132 = 670,761
26 × 32 × 7 × 132 = 681,408
22 × 34 × 133 = 711,828
24 × 3 × 7 × 133 = 738,192
23 × 34 × 7 × 132 = 766,584
25 × 3 × 72 × 132 = 794,976
24 × 34 × 72 × 13 = 825,552
2 × 33 × 7 × 133 = 830,466
23 × 72 × 133 = 861,224
26 × 34 × 132 = 876,096
22 × 33 × 72 × 132 = 894,348
24 × 33 × 133 = 949,104
32 × 72 × 133 = 968,877
26 × 7 × 133 = 984,256
25 × 33 × 7 × 132 = 1,022,112
26 × 33 × 72 × 13 = 1,100,736
23 × 32 × 7 × 133 = 1,107,288
24 × 32 × 72 × 132 = 1,192,464
34 × 7 × 133 = 1,245,699
26 × 32 × 133 = 1,265,472
22 × 3 × 72 × 133 = 1,291,836
2 × 34 × 72 × 132 = 1,341,522
23 × 34 × 133 = 1,423,656
25 × 3 × 7 × 133 = 1,476,384
24 × 34 × 7 × 132 = 1,533,168
26 × 3 × 72 × 132 = 1,589,952
25 × 34 × 72 × 13 = 1,651,104
22 × 33 × 7 × 133 = 1,660,932
24 × 72 × 133 = 1,722,448
23 × 33 × 72 × 132 = 1,788,696
25 × 33 × 133 = 1,898,208
2 × 32 × 72 × 133 = 1,937,754
26 × 33 × 7 × 132 = 2,044,224
24 × 32 × 7 × 133 = 2,214,576
25 × 32 × 72 × 132 = 2,384,928
2 × 34 × 7 × 133 = 2,491,398
23 × 3 × 72 × 133 = 2,583,672
22 × 34 × 72 × 132 = 2,683,044
24 × 34 × 133 = 2,847,312
33 × 72 × 133 = 2,906,631
26 × 3 × 7 × 133 = 2,952,768
25 × 34 × 7 × 132 = 3,066,336
26 × 34 × 72 × 13 = 3,302,208
23 × 33 × 7 × 133 = 3,321,864
25 × 72 × 133 = 3,444,896
24 × 33 × 72 × 132 = 3,577,392
26 × 33 × 133 = 3,796,416
22 × 32 × 72 × 133 = 3,875,508
25 × 32 × 7 × 133 = 4,429,152
26 × 32 × 72 × 132 = 4,769,856
22 × 34 × 7 × 133 = 4,982,796
24 × 3 × 72 × 133 = 5,167,344
23 × 34 × 72 × 132 = 5,366,088
25 × 34 × 133 = 5,694,624
2 × 33 × 72 × 133 = 5,813,262
26 × 34 × 7 × 132 = 6,132,672
24 × 33 × 7 × 133 = 6,643,728
26 × 72 × 133 = 6,889,792
25 × 33 × 72 × 132 = 7,154,784
23 × 32 × 72 × 133 = 7,751,016
34 × 72 × 133 = 8,719,893
26 × 32 × 7 × 133 = 8,858,304
23 × 34 × 7 × 133 = 9,965,592
25 × 3 × 72 × 133 = 10,334,688
24 × 34 × 72 × 132 = 10,732,176
26 × 34 × 133 = 11,389,248
22 × 33 × 72 × 133 = 11,626,524
25 × 33 × 7 × 133 = 13,287,456
26 × 33 × 72 × 132 = 14,309,568
24 × 32 × 72 × 133 = 15,502,032
2 × 34 × 72 × 133 = 17,439,786
24 × 34 × 7 × 133 = 19,931,184
26 × 3 × 72 × 133 = 20,669,376
25 × 34 × 72 × 132 = 21,464,352
23 × 33 × 72 × 133 = 23,253,048
26 × 33 × 7 × 133 = 26,574,912
25 × 32 × 72 × 133 = 31,004,064
22 × 34 × 72 × 133 = 34,879,572
25 × 34 × 7 × 133 = 39,862,368
26 × 34 × 72 × 132 = 42,928,704
24 × 33 × 72 × 133 = 46,506,096
26 × 32 × 72 × 133 = 62,008,128
23 × 34 × 72 × 133 = 69,759,144
26 × 34 × 7 × 133 = 79,724,736
25 × 33 × 72 × 133 = 93,012,192
24 × 34 × 72 × 133 = 139,518,288
26 × 33 × 72 × 133 = 186,024,384
25 × 34 × 72 × 133 = 279,036,576
26 × 34 × 72 × 133 = 558,073,152

The final answer:
(scroll down)

558,073,152 has 420 factors (divisors):
1; 2; 3; 4; 6; 7; 8; 9; 12; 13; 14; 16; 18; 21; 24; 26; 27; 28; 32; 36; 39; 42; 48; 49; 52; 54; 56; 63; 64; 72; 78; 81; 84; 91; 96; 98; 104; 108; 112; 117; 126; 144; 147; 156; 162; 168; 169; 182; 189; 192; 196; 208; 216; 224; 234; 252; 273; 288; 294; 312; 324; 336; 338; 351; 364; 378; 392; 416; 432; 441; 448; 468; 504; 507; 546; 567; 576; 588; 624; 637; 648; 672; 676; 702; 728; 756; 784; 819; 832; 864; 882; 936; 1,008; 1,014; 1,053; 1,092; 1,134; 1,176; 1,183; 1,248; 1,274; 1,296; 1,323; 1,344; 1,352; 1,404; 1,456; 1,512; 1,521; 1,568; 1,638; 1,728; 1,764; 1,872; 1,911; 2,016; 2,028; 2,106; 2,184; 2,197; 2,268; 2,352; 2,366; 2,457; 2,496; 2,548; 2,592; 2,646; 2,704; 2,808; 2,912; 3,024; 3,042; 3,136; 3,276; 3,528; 3,549; 3,744; 3,822; 3,969; 4,032; 4,056; 4,212; 4,368; 4,394; 4,536; 4,563; 4,704; 4,732; 4,914; 5,096; 5,184; 5,292; 5,408; 5,616; 5,733; 5,824; 6,048; 6,084; 6,552; 6,591; 7,056; 7,098; 7,371; 7,488; 7,644; 7,938; 8,112; 8,281; 8,424; 8,736; 8,788; 9,072; 9,126; 9,408; 9,464; 9,828; 10,192; 10,584; 10,647; 10,816; 11,232; 11,466; 12,096; 12,168; 13,104; 13,182; 13,689; 14,112; 14,196; 14,742; 15,288; 15,379; 15,876; 16,224; 16,562; 16,848; 17,199; 17,472; 17,576; 18,144; 18,252; 18,928; 19,656; 19,773; 20,384; 21,168; 21,294; 22,464; 22,932; 24,336; 24,843; 26,208; 26,364; 27,378; 28,224; 28,392; 29,484; 30,576; 30,758; 31,752; 31,941; 32,448; 33,124; 33,696; 34,398; 35,152; 36,288; 36,504; 37,856; 39,312; 39,546; 40,768; 42,336; 42,588; 45,864; 46,137; 48,672; 49,686; 51,597; 52,416; 52,728; 54,756; 56,784; 58,968; 59,319; 61,152; 61,516; 63,504; 63,882; 66,248; 67,392; 68,796; 70,304; 73,008; 74,529; 75,712; 78,624; 79,092; 84,672; 85,176; 91,728; 92,274; 95,823; 97,344; 99,372; 103,194; 105,456; 107,653; 109,512; 113,568; 117,936; 118,638; 122,304; 123,032; 127,008; 127,764; 132,496; 137,592; 138,411; 140,608; 146,016; 149,058; 157,248; 158,184; 170,352; 177,957; 183,456; 184,548; 191,646; 198,744; 206,388; 210,912; 215,306; 219,024; 223,587; 227,136; 235,872; 237,276; 246,064; 254,016; 255,528; 264,992; 275,184; 276,822; 292,032; 298,116; 316,368; 322,959; 340,704; 355,914; 366,912; 369,096; 383,292; 397,488; 412,776; 415,233; 421,824; 430,612; 438,048; 447,174; 471,744; 474,552; 492,128; 511,056; 529,984; 550,368; 553,644; 596,232; 632,736; 645,918; 670,761; 681,408; 711,828; 738,192; 766,584; 794,976; 825,552; 830,466; 861,224; 876,096; 894,348; 949,104; 968,877; 984,256; 1,022,112; 1,100,736; 1,107,288; 1,192,464; 1,245,699; 1,265,472; 1,291,836; 1,341,522; 1,423,656; 1,476,384; 1,533,168; 1,589,952; 1,651,104; 1,660,932; 1,722,448; 1,788,696; 1,898,208; 1,937,754; 2,044,224; 2,214,576; 2,384,928; 2,491,398; 2,583,672; 2,683,044; 2,847,312; 2,906,631; 2,952,768; 3,066,336; 3,302,208; 3,321,864; 3,444,896; 3,577,392; 3,796,416; 3,875,508; 4,429,152; 4,769,856; 4,982,796; 5,167,344; 5,366,088; 5,694,624; 5,813,262; 6,132,672; 6,643,728; 6,889,792; 7,154,784; 7,751,016; 8,719,893; 8,858,304; 9,965,592; 10,334,688; 10,732,176; 11,389,248; 11,626,524; 13,287,456; 14,309,568; 15,502,032; 17,439,786; 19,931,184; 20,669,376; 21,464,352; 23,253,048; 26,574,912; 31,004,064; 34,879,572; 39,862,368; 42,928,704; 46,506,096; 62,008,128; 69,759,144; 79,724,736; 93,012,192; 139,518,288; 186,024,384; 279,036,576 and 558,073,152
out of which 4 prime factors: 2; 3; 7 and 13
558,073,152 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 558,073,141?

» What are all the proper, improper and prime factors (divisors) of the number 558,073,155?


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

What are all the proper, improper and prime factors (all the divisors) of the number 558,073,152? How to calculate them? May 16 00:12 UTC (GMT)
What are all the common factors (all the divisors and the prime factors) of the numbers 2,780,267,490 and 0? How to calculate them? May 16 00:12 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 12,675,919? How to calculate them? May 16 00:12 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 5,303,026? How to calculate them? May 16 00:12 UTC (GMT)
What are all the common factors (all the divisors and the prime factors) of the numbers 1,502,226 and 0? How to calculate them? May 16 00:12 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 150,498,000? How to calculate them? May 16 00:12 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 4,327,830,012? How to calculate them? May 16 00:12 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 4,618,352? How to calculate them? May 16 00:12 UTC (GMT)
What are all the common factors (all the divisors and the prime factors) of the numbers 10,000,000,005 and 58? How to calculate them? May 16 00:12 UTC (GMT)
What are all the common factors (all the divisors and the prime factors) of the numbers 2,886,240 and 0? How to calculate them? May 16 00:12 UTC (GMT)
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".