Factors of 79,000,000,704. Calculator of Proper, Improper, Prime and Compound Divisors, if Any

All the factors (divisors) of the number 79,000,000,704. Connection with the prime factorization of the number

To find all the divisors of the number 79,000,000,704:

  • 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 79,000,000,704:

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


79,000,000,704 = 26 × 33 × 197 × 239 × 971
79,000,000,704 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 = (6 + 1) × (3 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 7 × 4 × 2 × 2 × 2 = 224

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

2. Multiply the prime factors of the number 79,000,000,704

  • 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
composite factor = 2 × 3 = 6
composite factor = 23 = 8
composite factor = 32 = 9
composite factor = 22 × 3 = 12
composite factor = 24 = 16
composite factor = 2 × 32 = 18
composite factor = 23 × 3 = 24
composite factor = 33 = 27
composite factor = 25 = 32
composite factor = 22 × 32 = 36
composite factor = 24 × 3 = 48
composite factor = 2 × 33 = 54
composite factor = 26 = 64
composite factor = 23 × 32 = 72
composite factor = 25 × 3 = 96
composite factor = 22 × 33 = 108
composite factor = 24 × 32 = 144
composite factor = 26 × 3 = 192
prime factor = 197
composite factor = 23 × 33 = 216
prime factor = 239
composite factor = 25 × 32 = 288
composite factor = 2 × 197 = 394
composite factor = 24 × 33 = 432
composite factor = 2 × 239 = 478
composite factor = 26 × 32 = 576
composite factor = 3 × 197 = 591
composite factor = 3 × 239 = 717
composite factor = 22 × 197 = 788
composite factor = 25 × 33 = 864
composite factor = 22 × 239 = 956
prime factor = 971
composite factor = 2 × 3 × 197 = 1,182
composite factor = 2 × 3 × 239 = 1,434
composite factor = 23 × 197 = 1,576
composite factor = 26 × 33 = 1,728
composite factor = 32 × 197 = 1,773
composite factor = 23 × 239 = 1,912
composite factor = 2 × 971 = 1,942
composite factor = 32 × 239 = 2,151
composite factor = 22 × 3 × 197 = 2,364
composite factor = 22 × 3 × 239 = 2,868
composite factor = 3 × 971 = 2,913
composite factor = 24 × 197 = 3,152
composite factor = 2 × 32 × 197 = 3,546
composite factor = 24 × 239 = 3,824
composite factor = 22 × 971 = 3,884
composite factor = 2 × 32 × 239 = 4,302
composite factor = 23 × 3 × 197 = 4,728
composite factor = 33 × 197 = 5,319
composite factor = 23 × 3 × 239 = 5,736
composite factor = 2 × 3 × 971 = 5,826
composite factor = 25 × 197 = 6,304
composite factor = 33 × 239 = 6,453
composite factor = 22 × 32 × 197 = 7,092
composite factor = 25 × 239 = 7,648
composite factor = 23 × 971 = 7,768
composite factor = 22 × 32 × 239 = 8,604
composite factor = 32 × 971 = 8,739
composite factor = 24 × 3 × 197 = 9,456
composite factor = 2 × 33 × 197 = 10,638
composite factor = 24 × 3 × 239 = 11,472
composite factor = 22 × 3 × 971 = 11,652
composite factor = 26 × 197 = 12,608
composite factor = 2 × 33 × 239 = 12,906
composite factor = 23 × 32 × 197 = 14,184
composite factor = 26 × 239 = 15,296
composite factor = 24 × 971 = 15,536
composite factor = 23 × 32 × 239 = 17,208
composite factor = 2 × 32 × 971 = 17,478
composite factor = 25 × 3 × 197 = 18,912
composite factor = 22 × 33 × 197 = 21,276
composite factor = 25 × 3 × 239 = 22,944
composite factor = 23 × 3 × 971 = 23,304
composite factor = 22 × 33 × 239 = 25,812
composite factor = 33 × 971 = 26,217
composite factor = 24 × 32 × 197 = 28,368
composite factor = 25 × 971 = 31,072
composite factor = 24 × 32 × 239 = 34,416
composite factor = 22 × 32 × 971 = 34,956
composite factor = 26 × 3 × 197 = 37,824
composite factor = 23 × 33 × 197 = 42,552
composite factor = 26 × 3 × 239 = 45,888
composite factor = 24 × 3 × 971 = 46,608
composite factor = 197 × 239 = 47,083
composite factor = 23 × 33 × 239 = 51,624
composite factor = 2 × 33 × 971 = 52,434
composite factor = 25 × 32 × 197 = 56,736
composite factor = 26 × 971 = 62,144
composite factor = 25 × 32 × 239 = 68,832
composite factor = 23 × 32 × 971 = 69,912
composite factor = 24 × 33 × 197 = 85,104
composite factor = 25 × 3 × 971 = 93,216
composite factor = 2 × 197 × 239 = 94,166
composite factor = 24 × 33 × 239 = 103,248
composite factor = 22 × 33 × 971 = 104,868
composite factor = 26 × 32 × 197 = 113,472
composite factor = 26 × 32 × 239 = 137,664
composite factor = 24 × 32 × 971 = 139,824
composite factor = 3 × 197 × 239 = 141,249
composite factor = 25 × 33 × 197 = 170,208
composite factor = 26 × 3 × 971 = 186,432
composite factor = 22 × 197 × 239 = 188,332
composite factor = 197 × 971 = 191,287
composite factor = 25 × 33 × 239 = 206,496
composite factor = 23 × 33 × 971 = 209,736
composite factor = 239 × 971 = 232,069
composite factor = 25 × 32 × 971 = 279,648
This list continues below...

... This list continues from above
composite factor = 2 × 3 × 197 × 239 = 282,498
composite factor = 26 × 33 × 197 = 340,416
composite factor = 23 × 197 × 239 = 376,664
composite factor = 2 × 197 × 971 = 382,574
composite factor = 26 × 33 × 239 = 412,992
composite factor = 24 × 33 × 971 = 419,472
composite factor = 32 × 197 × 239 = 423,747
composite factor = 2 × 239 × 971 = 464,138
composite factor = 26 × 32 × 971 = 559,296
composite factor = 22 × 3 × 197 × 239 = 564,996
composite factor = 3 × 197 × 971 = 573,861
composite factor = 3 × 239 × 971 = 696,207
composite factor = 24 × 197 × 239 = 753,328
composite factor = 22 × 197 × 971 = 765,148
composite factor = 25 × 33 × 971 = 838,944
composite factor = 2 × 32 × 197 × 239 = 847,494
composite factor = 22 × 239 × 971 = 928,276
composite factor = 23 × 3 × 197 × 239 = 1,129,992
composite factor = 2 × 3 × 197 × 971 = 1,147,722
composite factor = 33 × 197 × 239 = 1,271,241
composite factor = 2 × 3 × 239 × 971 = 1,392,414
composite factor = 25 × 197 × 239 = 1,506,656
composite factor = 23 × 197 × 971 = 1,530,296
composite factor = 26 × 33 × 971 = 1,677,888
composite factor = 22 × 32 × 197 × 239 = 1,694,988
composite factor = 32 × 197 × 971 = 1,721,583
composite factor = 23 × 239 × 971 = 1,856,552
composite factor = 32 × 239 × 971 = 2,088,621
composite factor = 24 × 3 × 197 × 239 = 2,259,984
composite factor = 22 × 3 × 197 × 971 = 2,295,444
composite factor = 2 × 33 × 197 × 239 = 2,542,482
composite factor = 22 × 3 × 239 × 971 = 2,784,828
composite factor = 26 × 197 × 239 = 3,013,312
composite factor = 24 × 197 × 971 = 3,060,592
composite factor = 23 × 32 × 197 × 239 = 3,389,976
composite factor = 2 × 32 × 197 × 971 = 3,443,166
composite factor = 24 × 239 × 971 = 3,713,104
composite factor = 2 × 32 × 239 × 971 = 4,177,242
composite factor = 25 × 3 × 197 × 239 = 4,519,968
composite factor = 23 × 3 × 197 × 971 = 4,590,888
composite factor = 22 × 33 × 197 × 239 = 5,084,964
composite factor = 33 × 197 × 971 = 5,164,749
composite factor = 23 × 3 × 239 × 971 = 5,569,656
composite factor = 25 × 197 × 971 = 6,121,184
composite factor = 33 × 239 × 971 = 6,265,863
composite factor = 24 × 32 × 197 × 239 = 6,779,952
composite factor = 22 × 32 × 197 × 971 = 6,886,332
composite factor = 25 × 239 × 971 = 7,426,208
composite factor = 22 × 32 × 239 × 971 = 8,354,484
composite factor = 26 × 3 × 197 × 239 = 9,039,936
composite factor = 24 × 3 × 197 × 971 = 9,181,776
composite factor = 23 × 33 × 197 × 239 = 10,169,928
composite factor = 2 × 33 × 197 × 971 = 10,329,498
composite factor = 24 × 3 × 239 × 971 = 11,139,312
composite factor = 26 × 197 × 971 = 12,242,368
composite factor = 2 × 33 × 239 × 971 = 12,531,726
composite factor = 25 × 32 × 197 × 239 = 13,559,904
composite factor = 23 × 32 × 197 × 971 = 13,772,664
composite factor = 26 × 239 × 971 = 14,852,416
composite factor = 23 × 32 × 239 × 971 = 16,708,968
composite factor = 25 × 3 × 197 × 971 = 18,363,552
composite factor = 24 × 33 × 197 × 239 = 20,339,856
composite factor = 22 × 33 × 197 × 971 = 20,658,996
composite factor = 25 × 3 × 239 × 971 = 22,278,624
composite factor = 22 × 33 × 239 × 971 = 25,063,452
composite factor = 26 × 32 × 197 × 239 = 27,119,808
composite factor = 24 × 32 × 197 × 971 = 27,545,328
composite factor = 24 × 32 × 239 × 971 = 33,417,936
composite factor = 26 × 3 × 197 × 971 = 36,727,104
composite factor = 25 × 33 × 197 × 239 = 40,679,712
composite factor = 23 × 33 × 197 × 971 = 41,317,992
composite factor = 26 × 3 × 239 × 971 = 44,557,248
composite factor = 197 × 239 × 971 = 45,717,593
composite factor = 23 × 33 × 239 × 971 = 50,126,904
composite factor = 25 × 32 × 197 × 971 = 55,090,656
composite factor = 25 × 32 × 239 × 971 = 66,835,872
composite factor = 26 × 33 × 197 × 239 = 81,359,424
composite factor = 24 × 33 × 197 × 971 = 82,635,984
composite factor = 2 × 197 × 239 × 971 = 91,435,186
composite factor = 24 × 33 × 239 × 971 = 100,253,808
composite factor = 26 × 32 × 197 × 971 = 110,181,312
composite factor = 26 × 32 × 239 × 971 = 133,671,744
composite factor = 3 × 197 × 239 × 971 = 137,152,779
composite factor = 25 × 33 × 197 × 971 = 165,271,968
composite factor = 22 × 197 × 239 × 971 = 182,870,372
composite factor = 25 × 33 × 239 × 971 = 200,507,616
composite factor = 2 × 3 × 197 × 239 × 971 = 274,305,558
composite factor = 26 × 33 × 197 × 971 = 330,543,936
composite factor = 23 × 197 × 239 × 971 = 365,740,744
composite factor = 26 × 33 × 239 × 971 = 401,015,232
composite factor = 32 × 197 × 239 × 971 = 411,458,337
composite factor = 22 × 3 × 197 × 239 × 971 = 548,611,116
composite factor = 24 × 197 × 239 × 971 = 731,481,488
composite factor = 2 × 32 × 197 × 239 × 971 = 822,916,674
composite factor = 23 × 3 × 197 × 239 × 971 = 1,097,222,232
composite factor = 33 × 197 × 239 × 971 = 1,234,375,011
composite factor = 25 × 197 × 239 × 971 = 1,462,962,976
composite factor = 22 × 32 × 197 × 239 × 971 = 1,645,833,348
composite factor = 24 × 3 × 197 × 239 × 971 = 2,194,444,464
composite factor = 2 × 33 × 197 × 239 × 971 = 2,468,750,022
composite factor = 26 × 197 × 239 × 971 = 2,925,925,952
composite factor = 23 × 32 × 197 × 239 × 971 = 3,291,666,696
composite factor = 25 × 3 × 197 × 239 × 971 = 4,388,888,928
composite factor = 22 × 33 × 197 × 239 × 971 = 4,937,500,044
composite factor = 24 × 32 × 197 × 239 × 971 = 6,583,333,392
composite factor = 26 × 3 × 197 × 239 × 971 = 8,777,777,856
composite factor = 23 × 33 × 197 × 239 × 971 = 9,875,000,088
composite factor = 25 × 32 × 197 × 239 × 971 = 13,166,666,784
composite factor = 24 × 33 × 197 × 239 × 971 = 19,750,000,176
composite factor = 26 × 32 × 197 × 239 × 971 = 26,333,333,568
composite factor = 25 × 33 × 197 × 239 × 971 = 39,500,000,352
composite factor = 26 × 33 × 197 × 239 × 971 = 79,000,000,704
224 factors (divisors)

What times what is 79,000,000,704?
What number multiplied by what number equals 79,000,000,704?

All the combinations of any two natural numbers whose product equals 79,000,000,704.

1 × 79,000,000,704 = 79,000,000,704
2 × 39,500,000,352 = 79,000,000,704
3 × 26,333,333,568 = 79,000,000,704
4 × 19,750,000,176 = 79,000,000,704
6 × 13,166,666,784 = 79,000,000,704
8 × 9,875,000,088 = 79,000,000,704
9 × 8,777,777,856 = 79,000,000,704
12 × 6,583,333,392 = 79,000,000,704
16 × 4,937,500,044 = 79,000,000,704
18 × 4,388,888,928 = 79,000,000,704
24 × 3,291,666,696 = 79,000,000,704
27 × 2,925,925,952 = 79,000,000,704
32 × 2,468,750,022 = 79,000,000,704
36 × 2,194,444,464 = 79,000,000,704
48 × 1,645,833,348 = 79,000,000,704
54 × 1,462,962,976 = 79,000,000,704
64 × 1,234,375,011 = 79,000,000,704
72 × 1,097,222,232 = 79,000,000,704
96 × 822,916,674 = 79,000,000,704
108 × 731,481,488 = 79,000,000,704
144 × 548,611,116 = 79,000,000,704
192 × 411,458,337 = 79,000,000,704
197 × 401,015,232 = 79,000,000,704
216 × 365,740,744 = 79,000,000,704
239 × 330,543,936 = 79,000,000,704
288 × 274,305,558 = 79,000,000,704
394 × 200,507,616 = 79,000,000,704
432 × 182,870,372 = 79,000,000,704
478 × 165,271,968 = 79,000,000,704
576 × 137,152,779 = 79,000,000,704
591 × 133,671,744 = 79,000,000,704
717 × 110,181,312 = 79,000,000,704
788 × 100,253,808 = 79,000,000,704
864 × 91,435,186 = 79,000,000,704
956 × 82,635,984 = 79,000,000,704
971 × 81,359,424 = 79,000,000,704
1,182 × 66,835,872 = 79,000,000,704
1,434 × 55,090,656 = 79,000,000,704
1,576 × 50,126,904 = 79,000,000,704
1,728 × 45,717,593 = 79,000,000,704
1,773 × 44,557,248 = 79,000,000,704
1,912 × 41,317,992 = 79,000,000,704
1,942 × 40,679,712 = 79,000,000,704
2,151 × 36,727,104 = 79,000,000,704
2,364 × 33,417,936 = 79,000,000,704
2,868 × 27,545,328 = 79,000,000,704
2,913 × 27,119,808 = 79,000,000,704
3,152 × 25,063,452 = 79,000,000,704
3,546 × 22,278,624 = 79,000,000,704
3,824 × 20,658,996 = 79,000,000,704
3,884 × 20,339,856 = 79,000,000,704
4,302 × 18,363,552 = 79,000,000,704
4,728 × 16,708,968 = 79,000,000,704
5,319 × 14,852,416 = 79,000,000,704
5,736 × 13,772,664 = 79,000,000,704
5,826 × 13,559,904 = 79,000,000,704
6,304 × 12,531,726 = 79,000,000,704
6,453 × 12,242,368 = 79,000,000,704
7,092 × 11,139,312 = 79,000,000,704
7,648 × 10,329,498 = 79,000,000,704
7,768 × 10,169,928 = 79,000,000,704
8,604 × 9,181,776 = 79,000,000,704
8,739 × 9,039,936 = 79,000,000,704
9,456 × 8,354,484 = 79,000,000,704
10,638 × 7,426,208 = 79,000,000,704
11,472 × 6,886,332 = 79,000,000,704
11,652 × 6,779,952 = 79,000,000,704
12,608 × 6,265,863 = 79,000,000,704
12,906 × 6,121,184 = 79,000,000,704
14,184 × 5,569,656 = 79,000,000,704
15,296 × 5,164,749 = 79,000,000,704
15,536 × 5,084,964 = 79,000,000,704
17,208 × 4,590,888 = 79,000,000,704
17,478 × 4,519,968 = 79,000,000,704
18,912 × 4,177,242 = 79,000,000,704
21,276 × 3,713,104 = 79,000,000,704
22,944 × 3,443,166 = 79,000,000,704
23,304 × 3,389,976 = 79,000,000,704
25,812 × 3,060,592 = 79,000,000,704
26,217 × 3,013,312 = 79,000,000,704
28,368 × 2,784,828 = 79,000,000,704
31,072 × 2,542,482 = 79,000,000,704
34,416 × 2,295,444 = 79,000,000,704
34,956 × 2,259,984 = 79,000,000,704
37,824 × 2,088,621 = 79,000,000,704
42,552 × 1,856,552 = 79,000,000,704
45,888 × 1,721,583 = 79,000,000,704
46,608 × 1,694,988 = 79,000,000,704
47,083 × 1,677,888 = 79,000,000,704
51,624 × 1,530,296 = 79,000,000,704
52,434 × 1,506,656 = 79,000,000,704
56,736 × 1,392,414 = 79,000,000,704
62,144 × 1,271,241 = 79,000,000,704
68,832 × 1,147,722 = 79,000,000,704
69,912 × 1,129,992 = 79,000,000,704
85,104 × 928,276 = 79,000,000,704
93,216 × 847,494 = 79,000,000,704
94,166 × 838,944 = 79,000,000,704
103,248 × 765,148 = 79,000,000,704
104,868 × 753,328 = 79,000,000,704
113,472 × 696,207 = 79,000,000,704
137,664 × 573,861 = 79,000,000,704
139,824 × 564,996 = 79,000,000,704
141,249 × 559,296 = 79,000,000,704
170,208 × 464,138 = 79,000,000,704
186,432 × 423,747 = 79,000,000,704
188,332 × 419,472 = 79,000,000,704
191,287 × 412,992 = 79,000,000,704
206,496 × 382,574 = 79,000,000,704
209,736 × 376,664 = 79,000,000,704
232,069 × 340,416 = 79,000,000,704
279,648 × 282,498 = 79,000,000,704
112 unique multiplications

The final answer:
(scroll down)


79,000,000,704 has 224 factors (divisors):
1; 2; 3; 4; 6; 8; 9; 12; 16; 18; 24; 27; 32; 36; 48; 54; 64; 72; 96; 108; 144; 192; 197; 216; 239; 288; 394; 432; 478; 576; 591; 717; 788; 864; 956; 971; 1,182; 1,434; 1,576; 1,728; 1,773; 1,912; 1,942; 2,151; 2,364; 2,868; 2,913; 3,152; 3,546; 3,824; 3,884; 4,302; 4,728; 5,319; 5,736; 5,826; 6,304; 6,453; 7,092; 7,648; 7,768; 8,604; 8,739; 9,456; 10,638; 11,472; 11,652; 12,608; 12,906; 14,184; 15,296; 15,536; 17,208; 17,478; 18,912; 21,276; 22,944; 23,304; 25,812; 26,217; 28,368; 31,072; 34,416; 34,956; 37,824; 42,552; 45,888; 46,608; 47,083; 51,624; 52,434; 56,736; 62,144; 68,832; 69,912; 85,104; 93,216; 94,166; 103,248; 104,868; 113,472; 137,664; 139,824; 141,249; 170,208; 186,432; 188,332; 191,287; 206,496; 209,736; 232,069; 279,648; 282,498; 340,416; 376,664; 382,574; 412,992; 419,472; 423,747; 464,138; 559,296; 564,996; 573,861; 696,207; 753,328; 765,148; 838,944; 847,494; 928,276; 1,129,992; 1,147,722; 1,271,241; 1,392,414; 1,506,656; 1,530,296; 1,677,888; 1,694,988; 1,721,583; 1,856,552; 2,088,621; 2,259,984; 2,295,444; 2,542,482; 2,784,828; 3,013,312; 3,060,592; 3,389,976; 3,443,166; 3,713,104; 4,177,242; 4,519,968; 4,590,888; 5,084,964; 5,164,749; 5,569,656; 6,121,184; 6,265,863; 6,779,952; 6,886,332; 7,426,208; 8,354,484; 9,039,936; 9,181,776; 10,169,928; 10,329,498; 11,139,312; 12,242,368; 12,531,726; 13,559,904; 13,772,664; 14,852,416; 16,708,968; 18,363,552; 20,339,856; 20,658,996; 22,278,624; 25,063,452; 27,119,808; 27,545,328; 33,417,936; 36,727,104; 40,679,712; 41,317,992; 44,557,248; 45,717,593; 50,126,904; 55,090,656; 66,835,872; 81,359,424; 82,635,984; 91,435,186; 100,253,808; 110,181,312; 133,671,744; 137,152,779; 165,271,968; 182,870,372; 200,507,616; 274,305,558; 330,543,936; 365,740,744; 401,015,232; 411,458,337; 548,611,116; 731,481,488; 822,916,674; 1,097,222,232; 1,234,375,011; 1,462,962,976; 1,645,833,348; 2,194,444,464; 2,468,750,022; 2,925,925,952; 3,291,666,696; 4,388,888,928; 4,937,500,044; 6,583,333,392; 8,777,777,856; 9,875,000,088; 13,166,666,784; 19,750,000,176; 26,333,333,568; 39,500,000,352 and 79,000,000,704
out of which 5 prime factors: 2; 3; 197; 239 and 971.
Numbers other than 1 that are not prime factors are composite factors (divisors).
79,000,000,704 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".