Given the Number 240,045,120, Calculate (Find) All the Factors (All the Divisors) of the Number 240,045,120 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 240,045,120

1. Carry out the prime factorization of the number 240,045,120:

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

240,045,120 = 26 × 37 × 5 × 73
240,045,120 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 240,045,120

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
2 × 7 = 14
3 × 5 = 15
24 = 16
2 × 32 = 18
22 × 5 = 20
3 × 7 = 21
23 × 3 = 24
33 = 27
22 × 7 = 28
2 × 3 × 5 = 30
25 = 32
5 × 7 = 35
22 × 32 = 36
23 × 5 = 40
2 × 3 × 7 = 42
32 × 5 = 45
24 × 3 = 48
72 = 49
2 × 33 = 54
23 × 7 = 56
22 × 3 × 5 = 60
32 × 7 = 63
26 = 64
2 × 5 × 7 = 70
23 × 32 = 72
24 × 5 = 80
34 = 81
22 × 3 × 7 = 84
2 × 32 × 5 = 90
25 × 3 = 96
2 × 72 = 98
3 × 5 × 7 = 105
22 × 33 = 108
24 × 7 = 112
23 × 3 × 5 = 120
2 × 32 × 7 = 126
33 × 5 = 135
22 × 5 × 7 = 140
24 × 32 = 144
3 × 72 = 147
25 × 5 = 160
2 × 34 = 162
23 × 3 × 7 = 168
22 × 32 × 5 = 180
33 × 7 = 189
26 × 3 = 192
22 × 72 = 196
2 × 3 × 5 × 7 = 210
23 × 33 = 216
25 × 7 = 224
24 × 3 × 5 = 240
35 = 243
5 × 72 = 245
22 × 32 × 7 = 252
2 × 33 × 5 = 270
23 × 5 × 7 = 280
25 × 32 = 288
2 × 3 × 72 = 294
32 × 5 × 7 = 315
26 × 5 = 320
22 × 34 = 324
24 × 3 × 7 = 336
73 = 343
23 × 32 × 5 = 360
2 × 33 × 7 = 378
23 × 72 = 392
34 × 5 = 405
22 × 3 × 5 × 7 = 420
24 × 33 = 432
32 × 72 = 441
26 × 7 = 448
25 × 3 × 5 = 480
2 × 35 = 486
2 × 5 × 72 = 490
23 × 32 × 7 = 504
22 × 33 × 5 = 540
24 × 5 × 7 = 560
34 × 7 = 567
26 × 32 = 576
22 × 3 × 72 = 588
2 × 32 × 5 × 7 = 630
23 × 34 = 648
25 × 3 × 7 = 672
2 × 73 = 686
24 × 32 × 5 = 720
36 = 729
3 × 5 × 72 = 735
22 × 33 × 7 = 756
24 × 72 = 784
2 × 34 × 5 = 810
23 × 3 × 5 × 7 = 840
25 × 33 = 864
2 × 32 × 72 = 882
33 × 5 × 7 = 945
26 × 3 × 5 = 960
22 × 35 = 972
22 × 5 × 72 = 980
24 × 32 × 7 = 1,008
3 × 73 = 1,029
23 × 33 × 5 = 1,080
25 × 5 × 7 = 1,120
2 × 34 × 7 = 1,134
23 × 3 × 72 = 1,176
35 × 5 = 1,215
22 × 32 × 5 × 7 = 1,260
24 × 34 = 1,296
33 × 72 = 1,323
26 × 3 × 7 = 1,344
22 × 73 = 1,372
25 × 32 × 5 = 1,440
2 × 36 = 1,458
2 × 3 × 5 × 72 = 1,470
23 × 33 × 7 = 1,512
25 × 72 = 1,568
22 × 34 × 5 = 1,620
24 × 3 × 5 × 7 = 1,680
35 × 7 = 1,701
5 × 73 = 1,715
26 × 33 = 1,728
22 × 32 × 72 = 1,764
2 × 33 × 5 × 7 = 1,890
23 × 35 = 1,944
23 × 5 × 72 = 1,960
25 × 32 × 7 = 2,016
2 × 3 × 73 = 2,058
24 × 33 × 5 = 2,160
37 = 2,187
32 × 5 × 72 = 2,205
26 × 5 × 7 = 2,240
22 × 34 × 7 = 2,268
24 × 3 × 72 = 2,352
2 × 35 × 5 = 2,430
23 × 32 × 5 × 7 = 2,520
25 × 34 = 2,592
2 × 33 × 72 = 2,646
23 × 73 = 2,744
34 × 5 × 7 = 2,835
26 × 32 × 5 = 2,880
22 × 36 = 2,916
22 × 3 × 5 × 72 = 2,940
24 × 33 × 7 = 3,024
32 × 73 = 3,087
26 × 72 = 3,136
23 × 34 × 5 = 3,240
25 × 3 × 5 × 7 = 3,360
2 × 35 × 7 = 3,402
2 × 5 × 73 = 3,430
23 × 32 × 72 = 3,528
36 × 5 = 3,645
22 × 33 × 5 × 7 = 3,780
24 × 35 = 3,888
24 × 5 × 72 = 3,920
34 × 72 = 3,969
26 × 32 × 7 = 4,032
22 × 3 × 73 = 4,116
25 × 33 × 5 = 4,320
2 × 37 = 4,374
2 × 32 × 5 × 72 = 4,410
23 × 34 × 7 = 4,536
25 × 3 × 72 = 4,704
22 × 35 × 5 = 4,860
24 × 32 × 5 × 7 = 5,040
36 × 7 = 5,103
3 × 5 × 73 = 5,145
26 × 34 = 5,184
22 × 33 × 72 = 5,292
24 × 73 = 5,488
2 × 34 × 5 × 7 = 5,670
23 × 36 = 5,832
23 × 3 × 5 × 72 = 5,880
25 × 33 × 7 = 6,048
2 × 32 × 73 = 6,174
24 × 34 × 5 = 6,480
33 × 5 × 72 = 6,615
26 × 3 × 5 × 7 = 6,720
22 × 35 × 7 = 6,804
22 × 5 × 73 = 6,860
24 × 32 × 72 = 7,056
2 × 36 × 5 = 7,290
23 × 33 × 5 × 7 = 7,560
25 × 35 = 7,776
25 × 5 × 72 = 7,840
2 × 34 × 72 = 7,938
23 × 3 × 73 = 8,232
35 × 5 × 7 = 8,505
26 × 33 × 5 = 8,640
22 × 37 = 8,748
22 × 32 × 5 × 72 = 8,820
24 × 34 × 7 = 9,072
33 × 73 = 9,261
26 × 3 × 72 = 9,408
23 × 35 × 5 = 9,720
25 × 32 × 5 × 7 = 10,080
2 × 36 × 7 = 10,206
2 × 3 × 5 × 73 = 10,290
23 × 33 × 72 = 10,584
37 × 5 = 10,935
25 × 73 = 10,976
22 × 34 × 5 × 7 = 11,340
24 × 36 = 11,664
24 × 3 × 5 × 72 = 11,760
35 × 72 = 11,907
26 × 33 × 7 = 12,096
22 × 32 × 73 = 12,348
25 × 34 × 5 = 12,960
2 × 33 × 5 × 72 = 13,230
23 × 35 × 7 = 13,608
23 × 5 × 73 = 13,720
25 × 32 × 72 = 14,112
22 × 36 × 5 = 14,580
24 × 33 × 5 × 7 = 15,120
37 × 7 = 15,309
32 × 5 × 73 = 15,435
This list continues below...

... This list continues from above
26 × 35 = 15,552
26 × 5 × 72 = 15,680
22 × 34 × 72 = 15,876
24 × 3 × 73 = 16,464
2 × 35 × 5 × 7 = 17,010
23 × 37 = 17,496
23 × 32 × 5 × 72 = 17,640
25 × 34 × 7 = 18,144
2 × 33 × 73 = 18,522
24 × 35 × 5 = 19,440
34 × 5 × 72 = 19,845
26 × 32 × 5 × 7 = 20,160
22 × 36 × 7 = 20,412
22 × 3 × 5 × 73 = 20,580
24 × 33 × 72 = 21,168
2 × 37 × 5 = 21,870
26 × 73 = 21,952
23 × 34 × 5 × 7 = 22,680
25 × 36 = 23,328
25 × 3 × 5 × 72 = 23,520
2 × 35 × 72 = 23,814
23 × 32 × 73 = 24,696
36 × 5 × 7 = 25,515
26 × 34 × 5 = 25,920
22 × 33 × 5 × 72 = 26,460
24 × 35 × 7 = 27,216
24 × 5 × 73 = 27,440
34 × 73 = 27,783
26 × 32 × 72 = 28,224
23 × 36 × 5 = 29,160
25 × 33 × 5 × 7 = 30,240
2 × 37 × 7 = 30,618
2 × 32 × 5 × 73 = 30,870
23 × 34 × 72 = 31,752
25 × 3 × 73 = 32,928
22 × 35 × 5 × 7 = 34,020
24 × 37 = 34,992
24 × 32 × 5 × 72 = 35,280
36 × 72 = 35,721
26 × 34 × 7 = 36,288
22 × 33 × 73 = 37,044
25 × 35 × 5 = 38,880
2 × 34 × 5 × 72 = 39,690
23 × 36 × 7 = 40,824
23 × 3 × 5 × 73 = 41,160
25 × 33 × 72 = 42,336
22 × 37 × 5 = 43,740
24 × 34 × 5 × 7 = 45,360
33 × 5 × 73 = 46,305
26 × 36 = 46,656
26 × 3 × 5 × 72 = 47,040
22 × 35 × 72 = 47,628
24 × 32 × 73 = 49,392
2 × 36 × 5 × 7 = 51,030
23 × 33 × 5 × 72 = 52,920
25 × 35 × 7 = 54,432
25 × 5 × 73 = 54,880
2 × 34 × 73 = 55,566
24 × 36 × 5 = 58,320
35 × 5 × 72 = 59,535
26 × 33 × 5 × 7 = 60,480
22 × 37 × 7 = 61,236
22 × 32 × 5 × 73 = 61,740
24 × 34 × 72 = 63,504
26 × 3 × 73 = 65,856
23 × 35 × 5 × 7 = 68,040
25 × 37 = 69,984
25 × 32 × 5 × 72 = 70,560
2 × 36 × 72 = 71,442
23 × 33 × 73 = 74,088
37 × 5 × 7 = 76,545
26 × 35 × 5 = 77,760
22 × 34 × 5 × 72 = 79,380
24 × 36 × 7 = 81,648
24 × 3 × 5 × 73 = 82,320
35 × 73 = 83,349
26 × 33 × 72 = 84,672
23 × 37 × 5 = 87,480
25 × 34 × 5 × 7 = 90,720
2 × 33 × 5 × 73 = 92,610
23 × 35 × 72 = 95,256
25 × 32 × 73 = 98,784
22 × 36 × 5 × 7 = 102,060
24 × 33 × 5 × 72 = 105,840
37 × 72 = 107,163
26 × 35 × 7 = 108,864
26 × 5 × 73 = 109,760
22 × 34 × 73 = 111,132
25 × 36 × 5 = 116,640
2 × 35 × 5 × 72 = 119,070
23 × 37 × 7 = 122,472
23 × 32 × 5 × 73 = 123,480
25 × 34 × 72 = 127,008
24 × 35 × 5 × 7 = 136,080
34 × 5 × 73 = 138,915
26 × 37 = 139,968
26 × 32 × 5 × 72 = 141,120
22 × 36 × 72 = 142,884
24 × 33 × 73 = 148,176
2 × 37 × 5 × 7 = 153,090
23 × 34 × 5 × 72 = 158,760
25 × 36 × 7 = 163,296
25 × 3 × 5 × 73 = 164,640
2 × 35 × 73 = 166,698
24 × 37 × 5 = 174,960
36 × 5 × 72 = 178,605
26 × 34 × 5 × 7 = 181,440
22 × 33 × 5 × 73 = 185,220
24 × 35 × 72 = 190,512
26 × 32 × 73 = 197,568
23 × 36 × 5 × 7 = 204,120
25 × 33 × 5 × 72 = 211,680
2 × 37 × 72 = 214,326
23 × 34 × 73 = 222,264
26 × 36 × 5 = 233,280
22 × 35 × 5 × 72 = 238,140
24 × 37 × 7 = 244,944
24 × 32 × 5 × 73 = 246,960
36 × 73 = 250,047
26 × 34 × 72 = 254,016
25 × 35 × 5 × 7 = 272,160
2 × 34 × 5 × 73 = 277,830
23 × 36 × 72 = 285,768
25 × 33 × 73 = 296,352
22 × 37 × 5 × 7 = 306,180
24 × 34 × 5 × 72 = 317,520
26 × 36 × 7 = 326,592
26 × 3 × 5 × 73 = 329,280
22 × 35 × 73 = 333,396
25 × 37 × 5 = 349,920
2 × 36 × 5 × 72 = 357,210
23 × 33 × 5 × 73 = 370,440
25 × 35 × 72 = 381,024
24 × 36 × 5 × 7 = 408,240
35 × 5 × 73 = 416,745
26 × 33 × 5 × 72 = 423,360
22 × 37 × 72 = 428,652
24 × 34 × 73 = 444,528
23 × 35 × 5 × 72 = 476,280
25 × 37 × 7 = 489,888
25 × 32 × 5 × 73 = 493,920
2 × 36 × 73 = 500,094
37 × 5 × 72 = 535,815
26 × 35 × 5 × 7 = 544,320
22 × 34 × 5 × 73 = 555,660
24 × 36 × 72 = 571,536
26 × 33 × 73 = 592,704
23 × 37 × 5 × 7 = 612,360
25 × 34 × 5 × 72 = 635,040
23 × 35 × 73 = 666,792
26 × 37 × 5 = 699,840
22 × 36 × 5 × 72 = 714,420
24 × 33 × 5 × 73 = 740,880
37 × 73 = 750,141
26 × 35 × 72 = 762,048
25 × 36 × 5 × 7 = 816,480
2 × 35 × 5 × 73 = 833,490
23 × 37 × 72 = 857,304
25 × 34 × 73 = 889,056
24 × 35 × 5 × 72 = 952,560
26 × 37 × 7 = 979,776
26 × 32 × 5 × 73 = 987,840
22 × 36 × 73 = 1,000,188
2 × 37 × 5 × 72 = 1,071,630
23 × 34 × 5 × 73 = 1,111,320
25 × 36 × 72 = 1,143,072
24 × 37 × 5 × 7 = 1,224,720
36 × 5 × 73 = 1,250,235
26 × 34 × 5 × 72 = 1,270,080
24 × 35 × 73 = 1,333,584
23 × 36 × 5 × 72 = 1,428,840
25 × 33 × 5 × 73 = 1,481,760
2 × 37 × 73 = 1,500,282
26 × 36 × 5 × 7 = 1,632,960
22 × 35 × 5 × 73 = 1,666,980
24 × 37 × 72 = 1,714,608
26 × 34 × 73 = 1,778,112
25 × 35 × 5 × 72 = 1,905,120
23 × 36 × 73 = 2,000,376
22 × 37 × 5 × 72 = 2,143,260
24 × 34 × 5 × 73 = 2,222,640
26 × 36 × 72 = 2,286,144
25 × 37 × 5 × 7 = 2,449,440
2 × 36 × 5 × 73 = 2,500,470
25 × 35 × 73 = 2,667,168
24 × 36 × 5 × 72 = 2,857,680
26 × 33 × 5 × 73 = 2,963,520
22 × 37 × 73 = 3,000,564
23 × 35 × 5 × 73 = 3,333,960
25 × 37 × 72 = 3,429,216
37 × 5 × 73 = 3,750,705
26 × 35 × 5 × 72 = 3,810,240
24 × 36 × 73 = 4,000,752
23 × 37 × 5 × 72 = 4,286,520
25 × 34 × 5 × 73 = 4,445,280
26 × 37 × 5 × 7 = 4,898,880
22 × 36 × 5 × 73 = 5,000,940
26 × 35 × 73 = 5,334,336
25 × 36 × 5 × 72 = 5,715,360
23 × 37 × 73 = 6,001,128
24 × 35 × 5 × 73 = 6,667,920
26 × 37 × 72 = 6,858,432
2 × 37 × 5 × 73 = 7,501,410
25 × 36 × 73 = 8,001,504
24 × 37 × 5 × 72 = 8,573,040
26 × 34 × 5 × 73 = 8,890,560
23 × 36 × 5 × 73 = 10,001,880
26 × 36 × 5 × 72 = 11,430,720
24 × 37 × 73 = 12,002,256
25 × 35 × 5 × 73 = 13,335,840
22 × 37 × 5 × 73 = 15,002,820
26 × 36 × 73 = 16,003,008
25 × 37 × 5 × 72 = 17,146,080
24 × 36 × 5 × 73 = 20,003,760
25 × 37 × 73 = 24,004,512
26 × 35 × 5 × 73 = 26,671,680
23 × 37 × 5 × 73 = 30,005,640
26 × 37 × 5 × 72 = 34,292,160
25 × 36 × 5 × 73 = 40,007,520
26 × 37 × 73 = 48,009,024
24 × 37 × 5 × 73 = 60,011,280
26 × 36 × 5 × 73 = 80,015,040
25 × 37 × 5 × 73 = 120,022,560
26 × 37 × 5 × 73 = 240,045,120

The final answer:
(scroll down)

240,045,120 has 448 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 12; 14; 15; 16; 18; 20; 21; 24; 27; 28; 30; 32; 35; 36; 40; 42; 45; 48; 49; 54; 56; 60; 63; 64; 70; 72; 80; 81; 84; 90; 96; 98; 105; 108; 112; 120; 126; 135; 140; 144; 147; 160; 162; 168; 180; 189; 192; 196; 210; 216; 224; 240; 243; 245; 252; 270; 280; 288; 294; 315; 320; 324; 336; 343; 360; 378; 392; 405; 420; 432; 441; 448; 480; 486; 490; 504; 540; 560; 567; 576; 588; 630; 648; 672; 686; 720; 729; 735; 756; 784; 810; 840; 864; 882; 945; 960; 972; 980; 1,008; 1,029; 1,080; 1,120; 1,134; 1,176; 1,215; 1,260; 1,296; 1,323; 1,344; 1,372; 1,440; 1,458; 1,470; 1,512; 1,568; 1,620; 1,680; 1,701; 1,715; 1,728; 1,764; 1,890; 1,944; 1,960; 2,016; 2,058; 2,160; 2,187; 2,205; 2,240; 2,268; 2,352; 2,430; 2,520; 2,592; 2,646; 2,744; 2,835; 2,880; 2,916; 2,940; 3,024; 3,087; 3,136; 3,240; 3,360; 3,402; 3,430; 3,528; 3,645; 3,780; 3,888; 3,920; 3,969; 4,032; 4,116; 4,320; 4,374; 4,410; 4,536; 4,704; 4,860; 5,040; 5,103; 5,145; 5,184; 5,292; 5,488; 5,670; 5,832; 5,880; 6,048; 6,174; 6,480; 6,615; 6,720; 6,804; 6,860; 7,056; 7,290; 7,560; 7,776; 7,840; 7,938; 8,232; 8,505; 8,640; 8,748; 8,820; 9,072; 9,261; 9,408; 9,720; 10,080; 10,206; 10,290; 10,584; 10,935; 10,976; 11,340; 11,664; 11,760; 11,907; 12,096; 12,348; 12,960; 13,230; 13,608; 13,720; 14,112; 14,580; 15,120; 15,309; 15,435; 15,552; 15,680; 15,876; 16,464; 17,010; 17,496; 17,640; 18,144; 18,522; 19,440; 19,845; 20,160; 20,412; 20,580; 21,168; 21,870; 21,952; 22,680; 23,328; 23,520; 23,814; 24,696; 25,515; 25,920; 26,460; 27,216; 27,440; 27,783; 28,224; 29,160; 30,240; 30,618; 30,870; 31,752; 32,928; 34,020; 34,992; 35,280; 35,721; 36,288; 37,044; 38,880; 39,690; 40,824; 41,160; 42,336; 43,740; 45,360; 46,305; 46,656; 47,040; 47,628; 49,392; 51,030; 52,920; 54,432; 54,880; 55,566; 58,320; 59,535; 60,480; 61,236; 61,740; 63,504; 65,856; 68,040; 69,984; 70,560; 71,442; 74,088; 76,545; 77,760; 79,380; 81,648; 82,320; 83,349; 84,672; 87,480; 90,720; 92,610; 95,256; 98,784; 102,060; 105,840; 107,163; 108,864; 109,760; 111,132; 116,640; 119,070; 122,472; 123,480; 127,008; 136,080; 138,915; 139,968; 141,120; 142,884; 148,176; 153,090; 158,760; 163,296; 164,640; 166,698; 174,960; 178,605; 181,440; 185,220; 190,512; 197,568; 204,120; 211,680; 214,326; 222,264; 233,280; 238,140; 244,944; 246,960; 250,047; 254,016; 272,160; 277,830; 285,768; 296,352; 306,180; 317,520; 326,592; 329,280; 333,396; 349,920; 357,210; 370,440; 381,024; 408,240; 416,745; 423,360; 428,652; 444,528; 476,280; 489,888; 493,920; 500,094; 535,815; 544,320; 555,660; 571,536; 592,704; 612,360; 635,040; 666,792; 699,840; 714,420; 740,880; 750,141; 762,048; 816,480; 833,490; 857,304; 889,056; 952,560; 979,776; 987,840; 1,000,188; 1,071,630; 1,111,320; 1,143,072; 1,224,720; 1,250,235; 1,270,080; 1,333,584; 1,428,840; 1,481,760; 1,500,282; 1,632,960; 1,666,980; 1,714,608; 1,778,112; 1,905,120; 2,000,376; 2,143,260; 2,222,640; 2,286,144; 2,449,440; 2,500,470; 2,667,168; 2,857,680; 2,963,520; 3,000,564; 3,333,960; 3,429,216; 3,750,705; 3,810,240; 4,000,752; 4,286,520; 4,445,280; 4,898,880; 5,000,940; 5,334,336; 5,715,360; 6,001,128; 6,667,920; 6,858,432; 7,501,410; 8,001,504; 8,573,040; 8,890,560; 10,001,880; 11,430,720; 12,002,256; 13,335,840; 15,002,820; 16,003,008; 17,146,080; 20,003,760; 24,004,512; 26,671,680; 30,005,640; 34,292,160; 40,007,520; 48,009,024; 60,011,280; 80,015,040; 120,022,560 and 240,045,120
out of which 4 prime factors: 2; 3; 5 and 7
240,045,120 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 240,045,109?

» What are all the proper, improper and prime factors (divisors) of the number 240,045,122?


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".