Given the Number 528,099,264, Calculate (Find) All the Factors (All the Divisors) of the Number 528,099,264 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 528,099,264

1. Carry out the prime factorization of the number 528,099,264:

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

528,099,264 = 26 × 37 × 73 × 11
528,099,264 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 528,099,264

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
prime factor = 11
22 × 3 = 12
2 × 7 = 14
24 = 16
2 × 32 = 18
3 × 7 = 21
2 × 11 = 22
23 × 3 = 24
33 = 27
22 × 7 = 28
25 = 32
3 × 11 = 33
22 × 32 = 36
2 × 3 × 7 = 42
22 × 11 = 44
24 × 3 = 48
72 = 49
2 × 33 = 54
23 × 7 = 56
32 × 7 = 63
26 = 64
2 × 3 × 11 = 66
23 × 32 = 72
7 × 11 = 77
34 = 81
22 × 3 × 7 = 84
23 × 11 = 88
25 × 3 = 96
2 × 72 = 98
32 × 11 = 99
22 × 33 = 108
24 × 7 = 112
2 × 32 × 7 = 126
22 × 3 × 11 = 132
24 × 32 = 144
3 × 72 = 147
2 × 7 × 11 = 154
2 × 34 = 162
23 × 3 × 7 = 168
24 × 11 = 176
33 × 7 = 189
26 × 3 = 192
22 × 72 = 196
2 × 32 × 11 = 198
23 × 33 = 216
25 × 7 = 224
3 × 7 × 11 = 231
35 = 243
22 × 32 × 7 = 252
23 × 3 × 11 = 264
25 × 32 = 288
2 × 3 × 72 = 294
33 × 11 = 297
22 × 7 × 11 = 308
22 × 34 = 324
24 × 3 × 7 = 336
73 = 343
25 × 11 = 352
2 × 33 × 7 = 378
23 × 72 = 392
22 × 32 × 11 = 396
24 × 33 = 432
32 × 72 = 441
26 × 7 = 448
2 × 3 × 7 × 11 = 462
2 × 35 = 486
23 × 32 × 7 = 504
24 × 3 × 11 = 528
72 × 11 = 539
34 × 7 = 567
26 × 32 = 576
22 × 3 × 72 = 588
2 × 33 × 11 = 594
23 × 7 × 11 = 616
23 × 34 = 648
25 × 3 × 7 = 672
2 × 73 = 686
32 × 7 × 11 = 693
26 × 11 = 704
36 = 729
22 × 33 × 7 = 756
24 × 72 = 784
23 × 32 × 11 = 792
25 × 33 = 864
2 × 32 × 72 = 882
34 × 11 = 891
22 × 3 × 7 × 11 = 924
22 × 35 = 972
24 × 32 × 7 = 1,008
3 × 73 = 1,029
25 × 3 × 11 = 1,056
2 × 72 × 11 = 1,078
2 × 34 × 7 = 1,134
23 × 3 × 72 = 1,176
22 × 33 × 11 = 1,188
24 × 7 × 11 = 1,232
24 × 34 = 1,296
33 × 72 = 1,323
26 × 3 × 7 = 1,344
22 × 73 = 1,372
2 × 32 × 7 × 11 = 1,386
2 × 36 = 1,458
23 × 33 × 7 = 1,512
25 × 72 = 1,568
24 × 32 × 11 = 1,584
3 × 72 × 11 = 1,617
35 × 7 = 1,701
26 × 33 = 1,728
22 × 32 × 72 = 1,764
2 × 34 × 11 = 1,782
23 × 3 × 7 × 11 = 1,848
23 × 35 = 1,944
25 × 32 × 7 = 2,016
2 × 3 × 73 = 2,058
33 × 7 × 11 = 2,079
26 × 3 × 11 = 2,112
22 × 72 × 11 = 2,156
37 = 2,187
22 × 34 × 7 = 2,268
24 × 3 × 72 = 2,352
23 × 33 × 11 = 2,376
25 × 7 × 11 = 2,464
25 × 34 = 2,592
2 × 33 × 72 = 2,646
35 × 11 = 2,673
23 × 73 = 2,744
22 × 32 × 7 × 11 = 2,772
22 × 36 = 2,916
24 × 33 × 7 = 3,024
32 × 73 = 3,087
26 × 72 = 3,136
25 × 32 × 11 = 3,168
2 × 3 × 72 × 11 = 3,234
2 × 35 × 7 = 3,402
23 × 32 × 72 = 3,528
22 × 34 × 11 = 3,564
24 × 3 × 7 × 11 = 3,696
73 × 11 = 3,773
24 × 35 = 3,888
34 × 72 = 3,969
26 × 32 × 7 = 4,032
22 × 3 × 73 = 4,116
2 × 33 × 7 × 11 = 4,158
23 × 72 × 11 = 4,312
2 × 37 = 4,374
23 × 34 × 7 = 4,536
25 × 3 × 72 = 4,704
24 × 33 × 11 = 4,752
32 × 72 × 11 = 4,851
26 × 7 × 11 = 4,928
36 × 7 = 5,103
26 × 34 = 5,184
22 × 33 × 72 = 5,292
2 × 35 × 11 = 5,346
24 × 73 = 5,488
23 × 32 × 7 × 11 = 5,544
23 × 36 = 5,832
25 × 33 × 7 = 6,048
2 × 32 × 73 = 6,174
34 × 7 × 11 = 6,237
26 × 32 × 11 = 6,336
22 × 3 × 72 × 11 = 6,468
22 × 35 × 7 = 6,804
24 × 32 × 72 = 7,056
23 × 34 × 11 = 7,128
25 × 3 × 7 × 11 = 7,392
2 × 73 × 11 = 7,546
25 × 35 = 7,776
2 × 34 × 72 = 7,938
36 × 11 = 8,019
23 × 3 × 73 = 8,232
22 × 33 × 7 × 11 = 8,316
24 × 72 × 11 = 8,624
22 × 37 = 8,748
24 × 34 × 7 = 9,072
33 × 73 = 9,261
26 × 3 × 72 = 9,408
25 × 33 × 11 = 9,504
2 × 32 × 72 × 11 = 9,702
2 × 36 × 7 = 10,206
23 × 33 × 72 = 10,584
22 × 35 × 11 = 10,692
25 × 73 = 10,976
24 × 32 × 7 × 11 = 11,088
3 × 73 × 11 = 11,319
24 × 36 = 11,664
35 × 72 = 11,907
26 × 33 × 7 = 12,096
22 × 32 × 73 = 12,348
2 × 34 × 7 × 11 = 12,474
23 × 3 × 72 × 11 = 12,936
23 × 35 × 7 = 13,608
25 × 32 × 72 = 14,112
24 × 34 × 11 = 14,256
33 × 72 × 11 = 14,553
26 × 3 × 7 × 11 = 14,784
22 × 73 × 11 = 15,092
37 × 7 = 15,309
26 × 35 = 15,552
22 × 34 × 72 = 15,876
2 × 36 × 11 = 16,038
24 × 3 × 73 = 16,464
23 × 33 × 7 × 11 = 16,632
25 × 72 × 11 = 17,248
23 × 37 = 17,496
25 × 34 × 7 = 18,144
2 × 33 × 73 = 18,522
35 × 7 × 11 = 18,711
26 × 33 × 11 = 19,008
22 × 32 × 72 × 11 = 19,404
22 × 36 × 7 = 20,412
24 × 33 × 72 = 21,168
23 × 35 × 11 = 21,384
26 × 73 = 21,952
25 × 32 × 7 × 11 = 22,176
2 × 3 × 73 × 11 = 22,638
This list continues below...

... This list continues from above
25 × 36 = 23,328
2 × 35 × 72 = 23,814
37 × 11 = 24,057
23 × 32 × 73 = 24,696
22 × 34 × 7 × 11 = 24,948
24 × 3 × 72 × 11 = 25,872
24 × 35 × 7 = 27,216
34 × 73 = 27,783
26 × 32 × 72 = 28,224
25 × 34 × 11 = 28,512
2 × 33 × 72 × 11 = 29,106
23 × 73 × 11 = 30,184
2 × 37 × 7 = 30,618
23 × 34 × 72 = 31,752
22 × 36 × 11 = 32,076
25 × 3 × 73 = 32,928
24 × 33 × 7 × 11 = 33,264
32 × 73 × 11 = 33,957
26 × 72 × 11 = 34,496
24 × 37 = 34,992
36 × 72 = 35,721
26 × 34 × 7 = 36,288
22 × 33 × 73 = 37,044
2 × 35 × 7 × 11 = 37,422
23 × 32 × 72 × 11 = 38,808
23 × 36 × 7 = 40,824
25 × 33 × 72 = 42,336
24 × 35 × 11 = 42,768
34 × 72 × 11 = 43,659
26 × 32 × 7 × 11 = 44,352
22 × 3 × 73 × 11 = 45,276
26 × 36 = 46,656
22 × 35 × 72 = 47,628
2 × 37 × 11 = 48,114
24 × 32 × 73 = 49,392
23 × 34 × 7 × 11 = 49,896
25 × 3 × 72 × 11 = 51,744
25 × 35 × 7 = 54,432
2 × 34 × 73 = 55,566
36 × 7 × 11 = 56,133
26 × 34 × 11 = 57,024
22 × 33 × 72 × 11 = 58,212
24 × 73 × 11 = 60,368
22 × 37 × 7 = 61,236
24 × 34 × 72 = 63,504
23 × 36 × 11 = 64,152
26 × 3 × 73 = 65,856
25 × 33 × 7 × 11 = 66,528
2 × 32 × 73 × 11 = 67,914
25 × 37 = 69,984
2 × 36 × 72 = 71,442
23 × 33 × 73 = 74,088
22 × 35 × 7 × 11 = 74,844
24 × 32 × 72 × 11 = 77,616
24 × 36 × 7 = 81,648
35 × 73 = 83,349
26 × 33 × 72 = 84,672
25 × 35 × 11 = 85,536
2 × 34 × 72 × 11 = 87,318
23 × 3 × 73 × 11 = 90,552
23 × 35 × 72 = 95,256
22 × 37 × 11 = 96,228
25 × 32 × 73 = 98,784
24 × 34 × 7 × 11 = 99,792
33 × 73 × 11 = 101,871
26 × 3 × 72 × 11 = 103,488
37 × 72 = 107,163
26 × 35 × 7 = 108,864
22 × 34 × 73 = 111,132
2 × 36 × 7 × 11 = 112,266
23 × 33 × 72 × 11 = 116,424
25 × 73 × 11 = 120,736
23 × 37 × 7 = 122,472
25 × 34 × 72 = 127,008
24 × 36 × 11 = 128,304
35 × 72 × 11 = 130,977
26 × 33 × 7 × 11 = 133,056
22 × 32 × 73 × 11 = 135,828
26 × 37 = 139,968
22 × 36 × 72 = 142,884
24 × 33 × 73 = 148,176
23 × 35 × 7 × 11 = 149,688
25 × 32 × 72 × 11 = 155,232
25 × 36 × 7 = 163,296
2 × 35 × 73 = 166,698
37 × 7 × 11 = 168,399
26 × 35 × 11 = 171,072
22 × 34 × 72 × 11 = 174,636
24 × 3 × 73 × 11 = 181,104
24 × 35 × 72 = 190,512
23 × 37 × 11 = 192,456
26 × 32 × 73 = 197,568
25 × 34 × 7 × 11 = 199,584
2 × 33 × 73 × 11 = 203,742
2 × 37 × 72 = 214,326
23 × 34 × 73 = 222,264
22 × 36 × 7 × 11 = 224,532
24 × 33 × 72 × 11 = 232,848
26 × 73 × 11 = 241,472
24 × 37 × 7 = 244,944
36 × 73 = 250,047
26 × 34 × 72 = 254,016
25 × 36 × 11 = 256,608
2 × 35 × 72 × 11 = 261,954
23 × 32 × 73 × 11 = 271,656
23 × 36 × 72 = 285,768
25 × 33 × 73 = 296,352
24 × 35 × 7 × 11 = 299,376
34 × 73 × 11 = 305,613
26 × 32 × 72 × 11 = 310,464
26 × 36 × 7 = 326,592
22 × 35 × 73 = 333,396
2 × 37 × 7 × 11 = 336,798
23 × 34 × 72 × 11 = 349,272
25 × 3 × 73 × 11 = 362,208
25 × 35 × 72 = 381,024
24 × 37 × 11 = 384,912
36 × 72 × 11 = 392,931
26 × 34 × 7 × 11 = 399,168
22 × 33 × 73 × 11 = 407,484
22 × 37 × 72 = 428,652
24 × 34 × 73 = 444,528
23 × 36 × 7 × 11 = 449,064
25 × 33 × 72 × 11 = 465,696
25 × 37 × 7 = 489,888
2 × 36 × 73 = 500,094
26 × 36 × 11 = 513,216
22 × 35 × 72 × 11 = 523,908
24 × 32 × 73 × 11 = 543,312
24 × 36 × 72 = 571,536
26 × 33 × 73 = 592,704
25 × 35 × 7 × 11 = 598,752
2 × 34 × 73 × 11 = 611,226
23 × 35 × 73 = 666,792
22 × 37 × 7 × 11 = 673,596
24 × 34 × 72 × 11 = 698,544
26 × 3 × 73 × 11 = 724,416
37 × 73 = 750,141
26 × 35 × 72 = 762,048
25 × 37 × 11 = 769,824
2 × 36 × 72 × 11 = 785,862
23 × 33 × 73 × 11 = 814,968
23 × 37 × 72 = 857,304
25 × 34 × 73 = 889,056
24 × 36 × 7 × 11 = 898,128
35 × 73 × 11 = 916,839
26 × 33 × 72 × 11 = 931,392
26 × 37 × 7 = 979,776
22 × 36 × 73 = 1,000,188
23 × 35 × 72 × 11 = 1,047,816
25 × 32 × 73 × 11 = 1,086,624
25 × 36 × 72 = 1,143,072
37 × 72 × 11 = 1,178,793
26 × 35 × 7 × 11 = 1,197,504
22 × 34 × 73 × 11 = 1,222,452
24 × 35 × 73 = 1,333,584
23 × 37 × 7 × 11 = 1,347,192
25 × 34 × 72 × 11 = 1,397,088
2 × 37 × 73 = 1,500,282
26 × 37 × 11 = 1,539,648
22 × 36 × 72 × 11 = 1,571,724
24 × 33 × 73 × 11 = 1,629,936
24 × 37 × 72 = 1,714,608
26 × 34 × 73 = 1,778,112
25 × 36 × 7 × 11 = 1,796,256
2 × 35 × 73 × 11 = 1,833,678
23 × 36 × 73 = 2,000,376
24 × 35 × 72 × 11 = 2,095,632
26 × 32 × 73 × 11 = 2,173,248
26 × 36 × 72 = 2,286,144
2 × 37 × 72 × 11 = 2,357,586
23 × 34 × 73 × 11 = 2,444,904
25 × 35 × 73 = 2,667,168
24 × 37 × 7 × 11 = 2,694,384
36 × 73 × 11 = 2,750,517
26 × 34 × 72 × 11 = 2,794,176
22 × 37 × 73 = 3,000,564
23 × 36 × 72 × 11 = 3,143,448
25 × 33 × 73 × 11 = 3,259,872
25 × 37 × 72 = 3,429,216
26 × 36 × 7 × 11 = 3,592,512
22 × 35 × 73 × 11 = 3,667,356
24 × 36 × 73 = 4,000,752
25 × 35 × 72 × 11 = 4,191,264
22 × 37 × 72 × 11 = 4,715,172
24 × 34 × 73 × 11 = 4,889,808
26 × 35 × 73 = 5,334,336
25 × 37 × 7 × 11 = 5,388,768
2 × 36 × 73 × 11 = 5,501,034
23 × 37 × 73 = 6,001,128
24 × 36 × 72 × 11 = 6,286,896
26 × 33 × 73 × 11 = 6,519,744
26 × 37 × 72 = 6,858,432
23 × 35 × 73 × 11 = 7,334,712
25 × 36 × 73 = 8,001,504
37 × 73 × 11 = 8,251,551
26 × 35 × 72 × 11 = 8,382,528
23 × 37 × 72 × 11 = 9,430,344
25 × 34 × 73 × 11 = 9,779,616
26 × 37 × 7 × 11 = 10,777,536
22 × 36 × 73 × 11 = 11,002,068
24 × 37 × 73 = 12,002,256
25 × 36 × 72 × 11 = 12,573,792
24 × 35 × 73 × 11 = 14,669,424
26 × 36 × 73 = 16,003,008
2 × 37 × 73 × 11 = 16,503,102
24 × 37 × 72 × 11 = 18,860,688
26 × 34 × 73 × 11 = 19,559,232
23 × 36 × 73 × 11 = 22,004,136
25 × 37 × 73 = 24,004,512
26 × 36 × 72 × 11 = 25,147,584
25 × 35 × 73 × 11 = 29,338,848
22 × 37 × 73 × 11 = 33,006,204
25 × 37 × 72 × 11 = 37,721,376
24 × 36 × 73 × 11 = 44,008,272
26 × 37 × 73 = 48,009,024
26 × 35 × 73 × 11 = 58,677,696
23 × 37 × 73 × 11 = 66,012,408
26 × 37 × 72 × 11 = 75,442,752
25 × 36 × 73 × 11 = 88,016,544
24 × 37 × 73 × 11 = 132,024,816
26 × 36 × 73 × 11 = 176,033,088
25 × 37 × 73 × 11 = 264,049,632
26 × 37 × 73 × 11 = 528,099,264

The final answer:
(scroll down)

528,099,264 has 448 factors (divisors):
1; 2; 3; 4; 6; 7; 8; 9; 11; 12; 14; 16; 18; 21; 22; 24; 27; 28; 32; 33; 36; 42; 44; 48; 49; 54; 56; 63; 64; 66; 72; 77; 81; 84; 88; 96; 98; 99; 108; 112; 126; 132; 144; 147; 154; 162; 168; 176; 189; 192; 196; 198; 216; 224; 231; 243; 252; 264; 288; 294; 297; 308; 324; 336; 343; 352; 378; 392; 396; 432; 441; 448; 462; 486; 504; 528; 539; 567; 576; 588; 594; 616; 648; 672; 686; 693; 704; 729; 756; 784; 792; 864; 882; 891; 924; 972; 1,008; 1,029; 1,056; 1,078; 1,134; 1,176; 1,188; 1,232; 1,296; 1,323; 1,344; 1,372; 1,386; 1,458; 1,512; 1,568; 1,584; 1,617; 1,701; 1,728; 1,764; 1,782; 1,848; 1,944; 2,016; 2,058; 2,079; 2,112; 2,156; 2,187; 2,268; 2,352; 2,376; 2,464; 2,592; 2,646; 2,673; 2,744; 2,772; 2,916; 3,024; 3,087; 3,136; 3,168; 3,234; 3,402; 3,528; 3,564; 3,696; 3,773; 3,888; 3,969; 4,032; 4,116; 4,158; 4,312; 4,374; 4,536; 4,704; 4,752; 4,851; 4,928; 5,103; 5,184; 5,292; 5,346; 5,488; 5,544; 5,832; 6,048; 6,174; 6,237; 6,336; 6,468; 6,804; 7,056; 7,128; 7,392; 7,546; 7,776; 7,938; 8,019; 8,232; 8,316; 8,624; 8,748; 9,072; 9,261; 9,408; 9,504; 9,702; 10,206; 10,584; 10,692; 10,976; 11,088; 11,319; 11,664; 11,907; 12,096; 12,348; 12,474; 12,936; 13,608; 14,112; 14,256; 14,553; 14,784; 15,092; 15,309; 15,552; 15,876; 16,038; 16,464; 16,632; 17,248; 17,496; 18,144; 18,522; 18,711; 19,008; 19,404; 20,412; 21,168; 21,384; 21,952; 22,176; 22,638; 23,328; 23,814; 24,057; 24,696; 24,948; 25,872; 27,216; 27,783; 28,224; 28,512; 29,106; 30,184; 30,618; 31,752; 32,076; 32,928; 33,264; 33,957; 34,496; 34,992; 35,721; 36,288; 37,044; 37,422; 38,808; 40,824; 42,336; 42,768; 43,659; 44,352; 45,276; 46,656; 47,628; 48,114; 49,392; 49,896; 51,744; 54,432; 55,566; 56,133; 57,024; 58,212; 60,368; 61,236; 63,504; 64,152; 65,856; 66,528; 67,914; 69,984; 71,442; 74,088; 74,844; 77,616; 81,648; 83,349; 84,672; 85,536; 87,318; 90,552; 95,256; 96,228; 98,784; 99,792; 101,871; 103,488; 107,163; 108,864; 111,132; 112,266; 116,424; 120,736; 122,472; 127,008; 128,304; 130,977; 133,056; 135,828; 139,968; 142,884; 148,176; 149,688; 155,232; 163,296; 166,698; 168,399; 171,072; 174,636; 181,104; 190,512; 192,456; 197,568; 199,584; 203,742; 214,326; 222,264; 224,532; 232,848; 241,472; 244,944; 250,047; 254,016; 256,608; 261,954; 271,656; 285,768; 296,352; 299,376; 305,613; 310,464; 326,592; 333,396; 336,798; 349,272; 362,208; 381,024; 384,912; 392,931; 399,168; 407,484; 428,652; 444,528; 449,064; 465,696; 489,888; 500,094; 513,216; 523,908; 543,312; 571,536; 592,704; 598,752; 611,226; 666,792; 673,596; 698,544; 724,416; 750,141; 762,048; 769,824; 785,862; 814,968; 857,304; 889,056; 898,128; 916,839; 931,392; 979,776; 1,000,188; 1,047,816; 1,086,624; 1,143,072; 1,178,793; 1,197,504; 1,222,452; 1,333,584; 1,347,192; 1,397,088; 1,500,282; 1,539,648; 1,571,724; 1,629,936; 1,714,608; 1,778,112; 1,796,256; 1,833,678; 2,000,376; 2,095,632; 2,173,248; 2,286,144; 2,357,586; 2,444,904; 2,667,168; 2,694,384; 2,750,517; 2,794,176; 3,000,564; 3,143,448; 3,259,872; 3,429,216; 3,592,512; 3,667,356; 4,000,752; 4,191,264; 4,715,172; 4,889,808; 5,334,336; 5,388,768; 5,501,034; 6,001,128; 6,286,896; 6,519,744; 6,858,432; 7,334,712; 8,001,504; 8,251,551; 8,382,528; 9,430,344; 9,779,616; 10,777,536; 11,002,068; 12,002,256; 12,573,792; 14,669,424; 16,003,008; 16,503,102; 18,860,688; 19,559,232; 22,004,136; 24,004,512; 25,147,584; 29,338,848; 33,006,204; 37,721,376; 44,008,272; 48,009,024; 58,677,696; 66,012,408; 75,442,752; 88,016,544; 132,024,816; 176,033,088; 264,049,632 and 528,099,264
out of which 4 prime factors: 2; 3; 7 and 11
528,099,264 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 528,099,262?

» What are all the proper, improper and prime factors (divisors) of the number 528,099,272?


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".