Factors of 2,368,080. Calculator of Proper, Improper, Prime and Compound Divisors, if Any

All the factors (divisors) of the number 2,368,080. Connection with the prime factorization of the number

To find all the divisors of the number 2,368,080:

  • 1. Decompose the number into prime factors.
  • See how you can find out how many factors (divisors) the number has, without actually calculating them.
  • 2. Multiply the prime factors in all their unique combinations, that yield different results.

1. Carry out the prime factorization of the number 2,368,080:

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


2,368,080 = 24 × 32 × 5 × 11 × 13 × 23
2,368,080 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.
  • Examples of prime numbers: 2 (factors 1, 2), 3 (factors 1, 3), 5 (factors 1, 5), 7 (factors 1, 7), 11 (factors 1, 11), 13 (factors 1, 13), ...
  • Composite number: a natural number that has at least one factor other than 1 and itself. So it is neither a prime number nor 1.
  • Examples of composite numbers: 4 (it has 3 factors: 1, 2, 4), 6 (it has 4 factors: 1, 2, 3, 6), 8 (it has 4 factors: 1, 2, 4, 8), 9 (it has 3 factors: 1, 3, 9), 10 (it has 4 factors: 1, 2, 5, 10), 12 (it has 6 factors: 1, 2, 3, 4, 6, 12), ...

  • » Online calculator. Check whether a number is prime or not. The prime factorization of composite numbers (decomposition into prime factors)


How to count the number of factors of a number?

Without actually finding the factors

  • If a number N is prime factorized as:
    N = am × bk × cz
    where a, b, c are the prime factors and m, k, z are their exponents, natural numbers, ....
  • ...
  • Then the number of factors of the number N can be calculated as:
    n = (m + 1) × (k + 1) × (z + 1)
  • ...
  • In our case, the number of factors is calculated as:
  • n = (4 + 1) × (2 + 1) × (1 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 5 × 3 × 2 × 2 × 2 × 2 = 240

But to actually calculate the factors, see below...

2. Multiply the prime factors of the number 2,368,080

  • 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):

Numbers other than 1 that are not prime factors are composite factors (divisors).

neither prime nor composite = 1
prime factor = 2
prime factor = 3
composite factor = 22 = 4
prime factor = 5
composite factor = 2 × 3 = 6
composite factor = 23 = 8
composite factor = 32 = 9
composite factor = 2 × 5 = 10
prime factor = 11
composite factor = 22 × 3 = 12
prime factor = 13
composite factor = 3 × 5 = 15
composite factor = 24 = 16
composite factor = 2 × 32 = 18
composite factor = 22 × 5 = 20
composite factor = 2 × 11 = 22
prime factor = 23
composite factor = 23 × 3 = 24
composite factor = 2 × 13 = 26
composite factor = 2 × 3 × 5 = 30
composite factor = 3 × 11 = 33
composite factor = 22 × 32 = 36
composite factor = 3 × 13 = 39
composite factor = 23 × 5 = 40
composite factor = 22 × 11 = 44
composite factor = 32 × 5 = 45
composite factor = 2 × 23 = 46
composite factor = 24 × 3 = 48
composite factor = 22 × 13 = 52
composite factor = 5 × 11 = 55
composite factor = 22 × 3 × 5 = 60
composite factor = 5 × 13 = 65
composite factor = 2 × 3 × 11 = 66
composite factor = 3 × 23 = 69
composite factor = 23 × 32 = 72
composite factor = 2 × 3 × 13 = 78
composite factor = 24 × 5 = 80
composite factor = 23 × 11 = 88
composite factor = 2 × 32 × 5 = 90
composite factor = 22 × 23 = 92
composite factor = 32 × 11 = 99
composite factor = 23 × 13 = 104
composite factor = 2 × 5 × 11 = 110
composite factor = 5 × 23 = 115
composite factor = 32 × 13 = 117
composite factor = 23 × 3 × 5 = 120
composite factor = 2 × 5 × 13 = 130
composite factor = 22 × 3 × 11 = 132
composite factor = 2 × 3 × 23 = 138
composite factor = 11 × 13 = 143
composite factor = 24 × 32 = 144
composite factor = 22 × 3 × 13 = 156
composite factor = 3 × 5 × 11 = 165
composite factor = 24 × 11 = 176
composite factor = 22 × 32 × 5 = 180
composite factor = 23 × 23 = 184
composite factor = 3 × 5 × 13 = 195
composite factor = 2 × 32 × 11 = 198
composite factor = 32 × 23 = 207
composite factor = 24 × 13 = 208
composite factor = 22 × 5 × 11 = 220
composite factor = 2 × 5 × 23 = 230
composite factor = 2 × 32 × 13 = 234
composite factor = 24 × 3 × 5 = 240
composite factor = 11 × 23 = 253
composite factor = 22 × 5 × 13 = 260
composite factor = 23 × 3 × 11 = 264
composite factor = 22 × 3 × 23 = 276
composite factor = 2 × 11 × 13 = 286
composite factor = 13 × 23 = 299
composite factor = 23 × 3 × 13 = 312
composite factor = 2 × 3 × 5 × 11 = 330
composite factor = 3 × 5 × 23 = 345
composite factor = 23 × 32 × 5 = 360
composite factor = 24 × 23 = 368
composite factor = 2 × 3 × 5 × 13 = 390
composite factor = 22 × 32 × 11 = 396
composite factor = 2 × 32 × 23 = 414
composite factor = 3 × 11 × 13 = 429
composite factor = 23 × 5 × 11 = 440
composite factor = 22 × 5 × 23 = 460
composite factor = 22 × 32 × 13 = 468
composite factor = 32 × 5 × 11 = 495
composite factor = 2 × 11 × 23 = 506
composite factor = 23 × 5 × 13 = 520
composite factor = 24 × 3 × 11 = 528
composite factor = 23 × 3 × 23 = 552
composite factor = 22 × 11 × 13 = 572
composite factor = 32 × 5 × 13 = 585
composite factor = 2 × 13 × 23 = 598
composite factor = 24 × 3 × 13 = 624
composite factor = 22 × 3 × 5 × 11 = 660
composite factor = 2 × 3 × 5 × 23 = 690
composite factor = 5 × 11 × 13 = 715
composite factor = 24 × 32 × 5 = 720
composite factor = 3 × 11 × 23 = 759
composite factor = 22 × 3 × 5 × 13 = 780
composite factor = 23 × 32 × 11 = 792
composite factor = 22 × 32 × 23 = 828
composite factor = 2 × 3 × 11 × 13 = 858
composite factor = 24 × 5 × 11 = 880
composite factor = 3 × 13 × 23 = 897
composite factor = 23 × 5 × 23 = 920
composite factor = 23 × 32 × 13 = 936
composite factor = 2 × 32 × 5 × 11 = 990
composite factor = 22 × 11 × 23 = 1,012
composite factor = 32 × 5 × 23 = 1,035
composite factor = 24 × 5 × 13 = 1,040
composite factor = 24 × 3 × 23 = 1,104
composite factor = 23 × 11 × 13 = 1,144
composite factor = 2 × 32 × 5 × 13 = 1,170
composite factor = 22 × 13 × 23 = 1,196
composite factor = 5 × 11 × 23 = 1,265
composite factor = 32 × 11 × 13 = 1,287
composite factor = 23 × 3 × 5 × 11 = 1,320
composite factor = 22 × 3 × 5 × 23 = 1,380
composite factor = 2 × 5 × 11 × 13 = 1,430
composite factor = 5 × 13 × 23 = 1,495
composite factor = 2 × 3 × 11 × 23 = 1,518
This list continues below...

... This list continues from above
composite factor = 23 × 3 × 5 × 13 = 1,560
composite factor = 24 × 32 × 11 = 1,584
composite factor = 23 × 32 × 23 = 1,656
composite factor = 22 × 3 × 11 × 13 = 1,716
composite factor = 2 × 3 × 13 × 23 = 1,794
composite factor = 24 × 5 × 23 = 1,840
composite factor = 24 × 32 × 13 = 1,872
composite factor = 22 × 32 × 5 × 11 = 1,980
composite factor = 23 × 11 × 23 = 2,024
composite factor = 2 × 32 × 5 × 23 = 2,070
composite factor = 3 × 5 × 11 × 13 = 2,145
composite factor = 32 × 11 × 23 = 2,277
composite factor = 24 × 11 × 13 = 2,288
composite factor = 22 × 32 × 5 × 13 = 2,340
composite factor = 23 × 13 × 23 = 2,392
composite factor = 2 × 5 × 11 × 23 = 2,530
composite factor = 2 × 32 × 11 × 13 = 2,574
composite factor = 24 × 3 × 5 × 11 = 2,640
composite factor = 32 × 13 × 23 = 2,691
composite factor = 23 × 3 × 5 × 23 = 2,760
composite factor = 22 × 5 × 11 × 13 = 2,860
composite factor = 2 × 5 × 13 × 23 = 2,990
composite factor = 22 × 3 × 11 × 23 = 3,036
composite factor = 24 × 3 × 5 × 13 = 3,120
composite factor = 11 × 13 × 23 = 3,289
composite factor = 24 × 32 × 23 = 3,312
composite factor = 23 × 3 × 11 × 13 = 3,432
composite factor = 22 × 3 × 13 × 23 = 3,588
composite factor = 3 × 5 × 11 × 23 = 3,795
composite factor = 23 × 32 × 5 × 11 = 3,960
composite factor = 24 × 11 × 23 = 4,048
composite factor = 22 × 32 × 5 × 23 = 4,140
composite factor = 2 × 3 × 5 × 11 × 13 = 4,290
composite factor = 3 × 5 × 13 × 23 = 4,485
composite factor = 2 × 32 × 11 × 23 = 4,554
composite factor = 23 × 32 × 5 × 13 = 4,680
composite factor = 24 × 13 × 23 = 4,784
composite factor = 22 × 5 × 11 × 23 = 5,060
composite factor = 22 × 32 × 11 × 13 = 5,148
composite factor = 2 × 32 × 13 × 23 = 5,382
composite factor = 24 × 3 × 5 × 23 = 5,520
composite factor = 23 × 5 × 11 × 13 = 5,720
composite factor = 22 × 5 × 13 × 23 = 5,980
composite factor = 23 × 3 × 11 × 23 = 6,072
composite factor = 32 × 5 × 11 × 13 = 6,435
composite factor = 2 × 11 × 13 × 23 = 6,578
composite factor = 24 × 3 × 11 × 13 = 6,864
composite factor = 23 × 3 × 13 × 23 = 7,176
composite factor = 2 × 3 × 5 × 11 × 23 = 7,590
composite factor = 24 × 32 × 5 × 11 = 7,920
composite factor = 23 × 32 × 5 × 23 = 8,280
composite factor = 22 × 3 × 5 × 11 × 13 = 8,580
composite factor = 2 × 3 × 5 × 13 × 23 = 8,970
composite factor = 22 × 32 × 11 × 23 = 9,108
composite factor = 24 × 32 × 5 × 13 = 9,360
composite factor = 3 × 11 × 13 × 23 = 9,867
composite factor = 23 × 5 × 11 × 23 = 10,120
composite factor = 23 × 32 × 11 × 13 = 10,296
composite factor = 22 × 32 × 13 × 23 = 10,764
composite factor = 32 × 5 × 11 × 23 = 11,385
composite factor = 24 × 5 × 11 × 13 = 11,440
composite factor = 23 × 5 × 13 × 23 = 11,960
composite factor = 24 × 3 × 11 × 23 = 12,144
composite factor = 2 × 32 × 5 × 11 × 13 = 12,870
composite factor = 22 × 11 × 13 × 23 = 13,156
composite factor = 32 × 5 × 13 × 23 = 13,455
composite factor = 24 × 3 × 13 × 23 = 14,352
composite factor = 22 × 3 × 5 × 11 × 23 = 15,180
composite factor = 5 × 11 × 13 × 23 = 16,445
composite factor = 24 × 32 × 5 × 23 = 16,560
composite factor = 23 × 3 × 5 × 11 × 13 = 17,160
composite factor = 22 × 3 × 5 × 13 × 23 = 17,940
composite factor = 23 × 32 × 11 × 23 = 18,216
composite factor = 2 × 3 × 11 × 13 × 23 = 19,734
composite factor = 24 × 5 × 11 × 23 = 20,240
composite factor = 24 × 32 × 11 × 13 = 20,592
composite factor = 23 × 32 × 13 × 23 = 21,528
composite factor = 2 × 32 × 5 × 11 × 23 = 22,770
composite factor = 24 × 5 × 13 × 23 = 23,920
composite factor = 22 × 32 × 5 × 11 × 13 = 25,740
composite factor = 23 × 11 × 13 × 23 = 26,312
composite factor = 2 × 32 × 5 × 13 × 23 = 26,910
composite factor = 32 × 11 × 13 × 23 = 29,601
composite factor = 23 × 3 × 5 × 11 × 23 = 30,360
composite factor = 2 × 5 × 11 × 13 × 23 = 32,890
composite factor = 24 × 3 × 5 × 11 × 13 = 34,320
composite factor = 23 × 3 × 5 × 13 × 23 = 35,880
composite factor = 24 × 32 × 11 × 23 = 36,432
composite factor = 22 × 3 × 11 × 13 × 23 = 39,468
composite factor = 24 × 32 × 13 × 23 = 43,056
composite factor = 22 × 32 × 5 × 11 × 23 = 45,540
composite factor = 3 × 5 × 11 × 13 × 23 = 49,335
composite factor = 23 × 32 × 5 × 11 × 13 = 51,480
composite factor = 24 × 11 × 13 × 23 = 52,624
composite factor = 22 × 32 × 5 × 13 × 23 = 53,820
composite factor = 2 × 32 × 11 × 13 × 23 = 59,202
composite factor = 24 × 3 × 5 × 11 × 23 = 60,720
composite factor = 22 × 5 × 11 × 13 × 23 = 65,780
composite factor = 24 × 3 × 5 × 13 × 23 = 71,760
composite factor = 23 × 3 × 11 × 13 × 23 = 78,936
composite factor = 23 × 32 × 5 × 11 × 23 = 91,080
composite factor = 2 × 3 × 5 × 11 × 13 × 23 = 98,670
composite factor = 24 × 32 × 5 × 11 × 13 = 102,960
composite factor = 23 × 32 × 5 × 13 × 23 = 107,640
composite factor = 22 × 32 × 11 × 13 × 23 = 118,404
composite factor = 23 × 5 × 11 × 13 × 23 = 131,560
composite factor = 32 × 5 × 11 × 13 × 23 = 148,005
composite factor = 24 × 3 × 11 × 13 × 23 = 157,872
composite factor = 24 × 32 × 5 × 11 × 23 = 182,160
composite factor = 22 × 3 × 5 × 11 × 13 × 23 = 197,340
composite factor = 24 × 32 × 5 × 13 × 23 = 215,280
composite factor = 23 × 32 × 11 × 13 × 23 = 236,808
composite factor = 24 × 5 × 11 × 13 × 23 = 263,120
composite factor = 2 × 32 × 5 × 11 × 13 × 23 = 296,010
composite factor = 23 × 3 × 5 × 11 × 13 × 23 = 394,680
composite factor = 24 × 32 × 11 × 13 × 23 = 473,616
composite factor = 22 × 32 × 5 × 11 × 13 × 23 = 592,020
composite factor = 24 × 3 × 5 × 11 × 13 × 23 = 789,360
composite factor = 23 × 32 × 5 × 11 × 13 × 23 = 1,184,040
composite factor = 24 × 32 × 5 × 11 × 13 × 23 = 2,368,080
240 factors (divisors)

What times what is 2,368,080?
What number multiplied by what number equals 2,368,080?

All the combinations of any two natural numbers whose product equals 2,368,080.

1 × 2,368,080 = 2,368,080
2 × 1,184,040 = 2,368,080
3 × 789,360 = 2,368,080
4 × 592,020 = 2,368,080
5 × 473,616 = 2,368,080
6 × 394,680 = 2,368,080
8 × 296,010 = 2,368,080
9 × 263,120 = 2,368,080
10 × 236,808 = 2,368,080
11 × 215,280 = 2,368,080
12 × 197,340 = 2,368,080
13 × 182,160 = 2,368,080
15 × 157,872 = 2,368,080
16 × 148,005 = 2,368,080
18 × 131,560 = 2,368,080
20 × 118,404 = 2,368,080
22 × 107,640 = 2,368,080
23 × 102,960 = 2,368,080
24 × 98,670 = 2,368,080
26 × 91,080 = 2,368,080
30 × 78,936 = 2,368,080
33 × 71,760 = 2,368,080
36 × 65,780 = 2,368,080
39 × 60,720 = 2,368,080
40 × 59,202 = 2,368,080
44 × 53,820 = 2,368,080
45 × 52,624 = 2,368,080
46 × 51,480 = 2,368,080
48 × 49,335 = 2,368,080
52 × 45,540 = 2,368,080
55 × 43,056 = 2,368,080
60 × 39,468 = 2,368,080
65 × 36,432 = 2,368,080
66 × 35,880 = 2,368,080
69 × 34,320 = 2,368,080
72 × 32,890 = 2,368,080
78 × 30,360 = 2,368,080
80 × 29,601 = 2,368,080
88 × 26,910 = 2,368,080
90 × 26,312 = 2,368,080
92 × 25,740 = 2,368,080
99 × 23,920 = 2,368,080
104 × 22,770 = 2,368,080
110 × 21,528 = 2,368,080
115 × 20,592 = 2,368,080
117 × 20,240 = 2,368,080
120 × 19,734 = 2,368,080
130 × 18,216 = 2,368,080
132 × 17,940 = 2,368,080
138 × 17,160 = 2,368,080
143 × 16,560 = 2,368,080
144 × 16,445 = 2,368,080
156 × 15,180 = 2,368,080
165 × 14,352 = 2,368,080
176 × 13,455 = 2,368,080
180 × 13,156 = 2,368,080
184 × 12,870 = 2,368,080
195 × 12,144 = 2,368,080
198 × 11,960 = 2,368,080
207 × 11,440 = 2,368,080
208 × 11,385 = 2,368,080
220 × 10,764 = 2,368,080
230 × 10,296 = 2,368,080
234 × 10,120 = 2,368,080
240 × 9,867 = 2,368,080
253 × 9,360 = 2,368,080
260 × 9,108 = 2,368,080
264 × 8,970 = 2,368,080
276 × 8,580 = 2,368,080
286 × 8,280 = 2,368,080
299 × 7,920 = 2,368,080
312 × 7,590 = 2,368,080
330 × 7,176 = 2,368,080
345 × 6,864 = 2,368,080
360 × 6,578 = 2,368,080
368 × 6,435 = 2,368,080
390 × 6,072 = 2,368,080
396 × 5,980 = 2,368,080
414 × 5,720 = 2,368,080
429 × 5,520 = 2,368,080
440 × 5,382 = 2,368,080
460 × 5,148 = 2,368,080
468 × 5,060 = 2,368,080
495 × 4,784 = 2,368,080
506 × 4,680 = 2,368,080
520 × 4,554 = 2,368,080
528 × 4,485 = 2,368,080
552 × 4,290 = 2,368,080
572 × 4,140 = 2,368,080
585 × 4,048 = 2,368,080
598 × 3,960 = 2,368,080
624 × 3,795 = 2,368,080
660 × 3,588 = 2,368,080
690 × 3,432 = 2,368,080
715 × 3,312 = 2,368,080
720 × 3,289 = 2,368,080
759 × 3,120 = 2,368,080
780 × 3,036 = 2,368,080
792 × 2,990 = 2,368,080
828 × 2,860 = 2,368,080
858 × 2,760 = 2,368,080
880 × 2,691 = 2,368,080
897 × 2,640 = 2,368,080
920 × 2,574 = 2,368,080
936 × 2,530 = 2,368,080
990 × 2,392 = 2,368,080
1,012 × 2,340 = 2,368,080
1,035 × 2,288 = 2,368,080
1,040 × 2,277 = 2,368,080
1,104 × 2,145 = 2,368,080
1,144 × 2,070 = 2,368,080
1,170 × 2,024 = 2,368,080
1,196 × 1,980 = 2,368,080
1,265 × 1,872 = 2,368,080
1,287 × 1,840 = 2,368,080
1,320 × 1,794 = 2,368,080
1,380 × 1,716 = 2,368,080
1,430 × 1,656 = 2,368,080
1,495 × 1,584 = 2,368,080
1,518 × 1,560 = 2,368,080
120 unique multiplications

The final answer:
(scroll down)


2,368,080 has 240 factors (divisors):
1; 2; 3; 4; 5; 6; 8; 9; 10; 11; 12; 13; 15; 16; 18; 20; 22; 23; 24; 26; 30; 33; 36; 39; 40; 44; 45; 46; 48; 52; 55; 60; 65; 66; 69; 72; 78; 80; 88; 90; 92; 99; 104; 110; 115; 117; 120; 130; 132; 138; 143; 144; 156; 165; 176; 180; 184; 195; 198; 207; 208; 220; 230; 234; 240; 253; 260; 264; 276; 286; 299; 312; 330; 345; 360; 368; 390; 396; 414; 429; 440; 460; 468; 495; 506; 520; 528; 552; 572; 585; 598; 624; 660; 690; 715; 720; 759; 780; 792; 828; 858; 880; 897; 920; 936; 990; 1,012; 1,035; 1,040; 1,104; 1,144; 1,170; 1,196; 1,265; 1,287; 1,320; 1,380; 1,430; 1,495; 1,518; 1,560; 1,584; 1,656; 1,716; 1,794; 1,840; 1,872; 1,980; 2,024; 2,070; 2,145; 2,277; 2,288; 2,340; 2,392; 2,530; 2,574; 2,640; 2,691; 2,760; 2,860; 2,990; 3,036; 3,120; 3,289; 3,312; 3,432; 3,588; 3,795; 3,960; 4,048; 4,140; 4,290; 4,485; 4,554; 4,680; 4,784; 5,060; 5,148; 5,382; 5,520; 5,720; 5,980; 6,072; 6,435; 6,578; 6,864; 7,176; 7,590; 7,920; 8,280; 8,580; 8,970; 9,108; 9,360; 9,867; 10,120; 10,296; 10,764; 11,385; 11,440; 11,960; 12,144; 12,870; 13,156; 13,455; 14,352; 15,180; 16,445; 16,560; 17,160; 17,940; 18,216; 19,734; 20,240; 20,592; 21,528; 22,770; 23,920; 25,740; 26,312; 26,910; 29,601; 30,360; 32,890; 34,320; 35,880; 36,432; 39,468; 43,056; 45,540; 49,335; 51,480; 52,624; 53,820; 59,202; 60,720; 65,780; 71,760; 78,936; 91,080; 98,670; 102,960; 107,640; 118,404; 131,560; 148,005; 157,872; 182,160; 197,340; 215,280; 236,808; 263,120; 296,010; 394,680; 473,616; 592,020; 789,360; 1,184,040 and 2,368,080
out of which 6 prime factors: 2; 3; 5; 11; 13 and 23.
Numbers other than 1 that are not prime factors are composite factors (divisors).
2,368,080 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.

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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".