Factors of 2,500,000,020. Calculator of Proper, Improper, Prime and Compound Divisors, if Any

All the factors (divisors) of the number 2,500,000,020. Connection with the prime factorization of the number

To find all the divisors of the number 2,500,000,020:

  • 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 2,500,000,020:

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


2,500,000,020 = 22 × 32 × 5 × 7 × 1092 × 167
2,500,000,020 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 = (2 + 1) × (2 + 1) × (1 + 1) × (1 + 1) × (2 + 1) × (1 + 1) = 3 × 3 × 2 × 2 × 3 × 2 = 216

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

2. Multiply the prime factors of the number 2,500,000,020

  • 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
prime factor = 7
composite factor = 32 = 9
composite factor = 2 × 5 = 10
composite factor = 22 × 3 = 12
composite factor = 2 × 7 = 14
composite factor = 3 × 5 = 15
composite factor = 2 × 32 = 18
composite factor = 22 × 5 = 20
composite factor = 3 × 7 = 21
composite factor = 22 × 7 = 28
composite factor = 2 × 3 × 5 = 30
composite factor = 5 × 7 = 35
composite factor = 22 × 32 = 36
composite factor = 2 × 3 × 7 = 42
composite factor = 32 × 5 = 45
composite factor = 22 × 3 × 5 = 60
composite factor = 32 × 7 = 63
composite factor = 2 × 5 × 7 = 70
composite factor = 22 × 3 × 7 = 84
composite factor = 2 × 32 × 5 = 90
composite factor = 3 × 5 × 7 = 105
prime factor = 109
composite factor = 2 × 32 × 7 = 126
composite factor = 22 × 5 × 7 = 140
prime factor = 167
composite factor = 22 × 32 × 5 = 180
composite factor = 2 × 3 × 5 × 7 = 210
composite factor = 2 × 109 = 218
composite factor = 22 × 32 × 7 = 252
composite factor = 32 × 5 × 7 = 315
composite factor = 3 × 109 = 327
composite factor = 2 × 167 = 334
composite factor = 22 × 3 × 5 × 7 = 420
composite factor = 22 × 109 = 436
composite factor = 3 × 167 = 501
composite factor = 5 × 109 = 545
composite factor = 2 × 32 × 5 × 7 = 630
composite factor = 2 × 3 × 109 = 654
composite factor = 22 × 167 = 668
composite factor = 7 × 109 = 763
composite factor = 5 × 167 = 835
composite factor = 32 × 109 = 981
composite factor = 2 × 3 × 167 = 1,002
composite factor = 2 × 5 × 109 = 1,090
composite factor = 7 × 167 = 1,169
composite factor = 22 × 32 × 5 × 7 = 1,260
composite factor = 22 × 3 × 109 = 1,308
composite factor = 32 × 167 = 1,503
composite factor = 2 × 7 × 109 = 1,526
composite factor = 3 × 5 × 109 = 1,635
composite factor = 2 × 5 × 167 = 1,670
composite factor = 2 × 32 × 109 = 1,962
composite factor = 22 × 3 × 167 = 2,004
composite factor = 22 × 5 × 109 = 2,180
composite factor = 3 × 7 × 109 = 2,289
composite factor = 2 × 7 × 167 = 2,338
composite factor = 3 × 5 × 167 = 2,505
composite factor = 2 × 32 × 167 = 3,006
composite factor = 22 × 7 × 109 = 3,052
composite factor = 2 × 3 × 5 × 109 = 3,270
composite factor = 22 × 5 × 167 = 3,340
composite factor = 3 × 7 × 167 = 3,507
composite factor = 5 × 7 × 109 = 3,815
composite factor = 22 × 32 × 109 = 3,924
composite factor = 2 × 3 × 7 × 109 = 4,578
composite factor = 22 × 7 × 167 = 4,676
composite factor = 32 × 5 × 109 = 4,905
composite factor = 2 × 3 × 5 × 167 = 5,010
composite factor = 5 × 7 × 167 = 5,845
composite factor = 22 × 32 × 167 = 6,012
composite factor = 22 × 3 × 5 × 109 = 6,540
composite factor = 32 × 7 × 109 = 6,867
composite factor = 2 × 3 × 7 × 167 = 7,014
composite factor = 32 × 5 × 167 = 7,515
composite factor = 2 × 5 × 7 × 109 = 7,630
composite factor = 22 × 3 × 7 × 109 = 9,156
composite factor = 2 × 32 × 5 × 109 = 9,810
composite factor = 22 × 3 × 5 × 167 = 10,020
composite factor = 32 × 7 × 167 = 10,521
composite factor = 3 × 5 × 7 × 109 = 11,445
composite factor = 2 × 5 × 7 × 167 = 11,690
composite factor = 1092 = 11,881
composite factor = 2 × 32 × 7 × 109 = 13,734
composite factor = 22 × 3 × 7 × 167 = 14,028
composite factor = 2 × 32 × 5 × 167 = 15,030
composite factor = 22 × 5 × 7 × 109 = 15,260
composite factor = 3 × 5 × 7 × 167 = 17,535
composite factor = 109 × 167 = 18,203
composite factor = 22 × 32 × 5 × 109 = 19,620
composite factor = 2 × 32 × 7 × 167 = 21,042
composite factor = 2 × 3 × 5 × 7 × 109 = 22,890
composite factor = 22 × 5 × 7 × 167 = 23,380
composite factor = 2 × 1092 = 23,762
composite factor = 22 × 32 × 7 × 109 = 27,468
composite factor = 22 × 32 × 5 × 167 = 30,060
composite factor = 32 × 5 × 7 × 109 = 34,335
composite factor = 2 × 3 × 5 × 7 × 167 = 35,070
composite factor = 3 × 1092 = 35,643
composite factor = 2 × 109 × 167 = 36,406
composite factor = 22 × 32 × 7 × 167 = 42,084
composite factor = 22 × 3 × 5 × 7 × 109 = 45,780
composite factor = 22 × 1092 = 47,524
This list continues below...

... This list continues from above
composite factor = 32 × 5 × 7 × 167 = 52,605
composite factor = 3 × 109 × 167 = 54,609
composite factor = 5 × 1092 = 59,405
composite factor = 2 × 32 × 5 × 7 × 109 = 68,670
composite factor = 22 × 3 × 5 × 7 × 167 = 70,140
composite factor = 2 × 3 × 1092 = 71,286
composite factor = 22 × 109 × 167 = 72,812
composite factor = 7 × 1092 = 83,167
composite factor = 5 × 109 × 167 = 91,015
composite factor = 2 × 32 × 5 × 7 × 167 = 105,210
composite factor = 32 × 1092 = 106,929
composite factor = 2 × 3 × 109 × 167 = 109,218
composite factor = 2 × 5 × 1092 = 118,810
composite factor = 7 × 109 × 167 = 127,421
composite factor = 22 × 32 × 5 × 7 × 109 = 137,340
composite factor = 22 × 3 × 1092 = 142,572
composite factor = 32 × 109 × 167 = 163,827
composite factor = 2 × 7 × 1092 = 166,334
composite factor = 3 × 5 × 1092 = 178,215
composite factor = 2 × 5 × 109 × 167 = 182,030
composite factor = 22 × 32 × 5 × 7 × 167 = 210,420
composite factor = 2 × 32 × 1092 = 213,858
composite factor = 22 × 3 × 109 × 167 = 218,436
composite factor = 22 × 5 × 1092 = 237,620
composite factor = 3 × 7 × 1092 = 249,501
composite factor = 2 × 7 × 109 × 167 = 254,842
composite factor = 3 × 5 × 109 × 167 = 273,045
composite factor = 2 × 32 × 109 × 167 = 327,654
composite factor = 22 × 7 × 1092 = 332,668
composite factor = 2 × 3 × 5 × 1092 = 356,430
composite factor = 22 × 5 × 109 × 167 = 364,060
composite factor = 3 × 7 × 109 × 167 = 382,263
composite factor = 5 × 7 × 1092 = 415,835
composite factor = 22 × 32 × 1092 = 427,716
composite factor = 2 × 3 × 7 × 1092 = 499,002
composite factor = 22 × 7 × 109 × 167 = 509,684
composite factor = 32 × 5 × 1092 = 534,645
composite factor = 2 × 3 × 5 × 109 × 167 = 546,090
composite factor = 5 × 7 × 109 × 167 = 637,105
composite factor = 22 × 32 × 109 × 167 = 655,308
composite factor = 22 × 3 × 5 × 1092 = 712,860
composite factor = 32 × 7 × 1092 = 748,503
composite factor = 2 × 3 × 7 × 109 × 167 = 764,526
composite factor = 32 × 5 × 109 × 167 = 819,135
composite factor = 2 × 5 × 7 × 1092 = 831,670
composite factor = 22 × 3 × 7 × 1092 = 998,004
composite factor = 2 × 32 × 5 × 1092 = 1,069,290
composite factor = 22 × 3 × 5 × 109 × 167 = 1,092,180
composite factor = 32 × 7 × 109 × 167 = 1,146,789
composite factor = 3 × 5 × 7 × 1092 = 1,247,505
composite factor = 2 × 5 × 7 × 109 × 167 = 1,274,210
composite factor = 2 × 32 × 7 × 1092 = 1,497,006
composite factor = 22 × 3 × 7 × 109 × 167 = 1,529,052
composite factor = 2 × 32 × 5 × 109 × 167 = 1,638,270
composite factor = 22 × 5 × 7 × 1092 = 1,663,340
composite factor = 3 × 5 × 7 × 109 × 167 = 1,911,315
composite factor = 1092 × 167 = 1,984,127
composite factor = 22 × 32 × 5 × 1092 = 2,138,580
composite factor = 2 × 32 × 7 × 109 × 167 = 2,293,578
composite factor = 2 × 3 × 5 × 7 × 1092 = 2,495,010
composite factor = 22 × 5 × 7 × 109 × 167 = 2,548,420
composite factor = 22 × 32 × 7 × 1092 = 2,994,012
composite factor = 22 × 32 × 5 × 109 × 167 = 3,276,540
composite factor = 32 × 5 × 7 × 1092 = 3,742,515
composite factor = 2 × 3 × 5 × 7 × 109 × 167 = 3,822,630
composite factor = 2 × 1092 × 167 = 3,968,254
composite factor = 22 × 32 × 7 × 109 × 167 = 4,587,156
composite factor = 22 × 3 × 5 × 7 × 1092 = 4,990,020
composite factor = 32 × 5 × 7 × 109 × 167 = 5,733,945
composite factor = 3 × 1092 × 167 = 5,952,381
composite factor = 2 × 32 × 5 × 7 × 1092 = 7,485,030
composite factor = 22 × 3 × 5 × 7 × 109 × 167 = 7,645,260
composite factor = 22 × 1092 × 167 = 7,936,508
composite factor = 5 × 1092 × 167 = 9,920,635
composite factor = 2 × 32 × 5 × 7 × 109 × 167 = 11,467,890
composite factor = 2 × 3 × 1092 × 167 = 11,904,762
composite factor = 7 × 1092 × 167 = 13,888,889
composite factor = 22 × 32 × 5 × 7 × 1092 = 14,970,060
composite factor = 32 × 1092 × 167 = 17,857,143
composite factor = 2 × 5 × 1092 × 167 = 19,841,270
composite factor = 22 × 32 × 5 × 7 × 109 × 167 = 22,935,780
composite factor = 22 × 3 × 1092 × 167 = 23,809,524
composite factor = 2 × 7 × 1092 × 167 = 27,777,778
composite factor = 3 × 5 × 1092 × 167 = 29,761,905
composite factor = 2 × 32 × 1092 × 167 = 35,714,286
composite factor = 22 × 5 × 1092 × 167 = 39,682,540
composite factor = 3 × 7 × 1092 × 167 = 41,666,667
composite factor = 22 × 7 × 1092 × 167 = 55,555,556
composite factor = 2 × 3 × 5 × 1092 × 167 = 59,523,810
composite factor = 5 × 7 × 1092 × 167 = 69,444,445
composite factor = 22 × 32 × 1092 × 167 = 71,428,572
composite factor = 2 × 3 × 7 × 1092 × 167 = 83,333,334
composite factor = 32 × 5 × 1092 × 167 = 89,285,715
composite factor = 22 × 3 × 5 × 1092 × 167 = 119,047,620
composite factor = 32 × 7 × 1092 × 167 = 125,000,001
composite factor = 2 × 5 × 7 × 1092 × 167 = 138,888,890
composite factor = 22 × 3 × 7 × 1092 × 167 = 166,666,668
composite factor = 2 × 32 × 5 × 1092 × 167 = 178,571,430
composite factor = 3 × 5 × 7 × 1092 × 167 = 208,333,335
composite factor = 2 × 32 × 7 × 1092 × 167 = 250,000,002
composite factor = 22 × 5 × 7 × 1092 × 167 = 277,777,780
composite factor = 22 × 32 × 5 × 1092 × 167 = 357,142,860
composite factor = 2 × 3 × 5 × 7 × 1092 × 167 = 416,666,670
composite factor = 22 × 32 × 7 × 1092 × 167 = 500,000,004
composite factor = 32 × 5 × 7 × 1092 × 167 = 625,000,005
composite factor = 22 × 3 × 5 × 7 × 1092 × 167 = 833,333,340
composite factor = 2 × 32 × 5 × 7 × 1092 × 167 = 1,250,000,010
composite factor = 22 × 32 × 5 × 7 × 1092 × 167 = 2,500,000,020
216 factors (divisors)

What times what is 2,500,000,020?
What number multiplied by what number equals 2,500,000,020?

All the combinations of any two natural numbers whose product equals 2,500,000,020.

1 × 2,500,000,020 = 2,500,000,020
2 × 1,250,000,010 = 2,500,000,020
3 × 833,333,340 = 2,500,000,020
4 × 625,000,005 = 2,500,000,020
5 × 500,000,004 = 2,500,000,020
6 × 416,666,670 = 2,500,000,020
7 × 357,142,860 = 2,500,000,020
9 × 277,777,780 = 2,500,000,020
10 × 250,000,002 = 2,500,000,020
12 × 208,333,335 = 2,500,000,020
14 × 178,571,430 = 2,500,000,020
15 × 166,666,668 = 2,500,000,020
18 × 138,888,890 = 2,500,000,020
20 × 125,000,001 = 2,500,000,020
21 × 119,047,620 = 2,500,000,020
28 × 89,285,715 = 2,500,000,020
30 × 83,333,334 = 2,500,000,020
35 × 71,428,572 = 2,500,000,020
36 × 69,444,445 = 2,500,000,020
42 × 59,523,810 = 2,500,000,020
45 × 55,555,556 = 2,500,000,020
60 × 41,666,667 = 2,500,000,020
63 × 39,682,540 = 2,500,000,020
70 × 35,714,286 = 2,500,000,020
84 × 29,761,905 = 2,500,000,020
90 × 27,777,778 = 2,500,000,020
105 × 23,809,524 = 2,500,000,020
109 × 22,935,780 = 2,500,000,020
126 × 19,841,270 = 2,500,000,020
140 × 17,857,143 = 2,500,000,020
167 × 14,970,060 = 2,500,000,020
180 × 13,888,889 = 2,500,000,020
210 × 11,904,762 = 2,500,000,020
218 × 11,467,890 = 2,500,000,020
252 × 9,920,635 = 2,500,000,020
315 × 7,936,508 = 2,500,000,020
327 × 7,645,260 = 2,500,000,020
334 × 7,485,030 = 2,500,000,020
420 × 5,952,381 = 2,500,000,020
436 × 5,733,945 = 2,500,000,020
501 × 4,990,020 = 2,500,000,020
545 × 4,587,156 = 2,500,000,020
630 × 3,968,254 = 2,500,000,020
654 × 3,822,630 = 2,500,000,020
668 × 3,742,515 = 2,500,000,020
763 × 3,276,540 = 2,500,000,020
835 × 2,994,012 = 2,500,000,020
981 × 2,548,420 = 2,500,000,020
1,002 × 2,495,010 = 2,500,000,020
1,090 × 2,293,578 = 2,500,000,020
1,169 × 2,138,580 = 2,500,000,020
1,260 × 1,984,127 = 2,500,000,020
1,308 × 1,911,315 = 2,500,000,020
1,503 × 1,663,340 = 2,500,000,020
1,526 × 1,638,270 = 2,500,000,020
1,635 × 1,529,052 = 2,500,000,020
1,670 × 1,497,006 = 2,500,000,020
1,962 × 1,274,210 = 2,500,000,020
2,004 × 1,247,505 = 2,500,000,020
2,180 × 1,146,789 = 2,500,000,020
2,289 × 1,092,180 = 2,500,000,020
2,338 × 1,069,290 = 2,500,000,020
2,505 × 998,004 = 2,500,000,020
3,006 × 831,670 = 2,500,000,020
3,052 × 819,135 = 2,500,000,020
3,270 × 764,526 = 2,500,000,020
3,340 × 748,503 = 2,500,000,020
3,507 × 712,860 = 2,500,000,020
3,815 × 655,308 = 2,500,000,020
3,924 × 637,105 = 2,500,000,020
4,578 × 546,090 = 2,500,000,020
4,676 × 534,645 = 2,500,000,020
4,905 × 509,684 = 2,500,000,020
5,010 × 499,002 = 2,500,000,020
5,845 × 427,716 = 2,500,000,020
6,012 × 415,835 = 2,500,000,020
6,540 × 382,263 = 2,500,000,020
6,867 × 364,060 = 2,500,000,020
7,014 × 356,430 = 2,500,000,020
7,515 × 332,668 = 2,500,000,020
7,630 × 327,654 = 2,500,000,020
9,156 × 273,045 = 2,500,000,020
9,810 × 254,842 = 2,500,000,020
10,020 × 249,501 = 2,500,000,020
10,521 × 237,620 = 2,500,000,020
11,445 × 218,436 = 2,500,000,020
11,690 × 213,858 = 2,500,000,020
11,881 × 210,420 = 2,500,000,020
13,734 × 182,030 = 2,500,000,020
14,028 × 178,215 = 2,500,000,020
15,030 × 166,334 = 2,500,000,020
15,260 × 163,827 = 2,500,000,020
17,535 × 142,572 = 2,500,000,020
18,203 × 137,340 = 2,500,000,020
19,620 × 127,421 = 2,500,000,020
21,042 × 118,810 = 2,500,000,020
22,890 × 109,218 = 2,500,000,020
23,380 × 106,929 = 2,500,000,020
23,762 × 105,210 = 2,500,000,020
27,468 × 91,015 = 2,500,000,020
30,060 × 83,167 = 2,500,000,020
34,335 × 72,812 = 2,500,000,020
35,070 × 71,286 = 2,500,000,020
35,643 × 70,140 = 2,500,000,020
36,406 × 68,670 = 2,500,000,020
42,084 × 59,405 = 2,500,000,020
45,780 × 54,609 = 2,500,000,020
47,524 × 52,605 = 2,500,000,020
108 unique multiplications

The final answer:
(scroll down)


2,500,000,020 has 216 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 9; 10; 12; 14; 15; 18; 20; 21; 28; 30; 35; 36; 42; 45; 60; 63; 70; 84; 90; 105; 109; 126; 140; 167; 180; 210; 218; 252; 315; 327; 334; 420; 436; 501; 545; 630; 654; 668; 763; 835; 981; 1,002; 1,090; 1,169; 1,260; 1,308; 1,503; 1,526; 1,635; 1,670; 1,962; 2,004; 2,180; 2,289; 2,338; 2,505; 3,006; 3,052; 3,270; 3,340; 3,507; 3,815; 3,924; 4,578; 4,676; 4,905; 5,010; 5,845; 6,012; 6,540; 6,867; 7,014; 7,515; 7,630; 9,156; 9,810; 10,020; 10,521; 11,445; 11,690; 11,881; 13,734; 14,028; 15,030; 15,260; 17,535; 18,203; 19,620; 21,042; 22,890; 23,380; 23,762; 27,468; 30,060; 34,335; 35,070; 35,643; 36,406; 42,084; 45,780; 47,524; 52,605; 54,609; 59,405; 68,670; 70,140; 71,286; 72,812; 83,167; 91,015; 105,210; 106,929; 109,218; 118,810; 127,421; 137,340; 142,572; 163,827; 166,334; 178,215; 182,030; 210,420; 213,858; 218,436; 237,620; 249,501; 254,842; 273,045; 327,654; 332,668; 356,430; 364,060; 382,263; 415,835; 427,716; 499,002; 509,684; 534,645; 546,090; 637,105; 655,308; 712,860; 748,503; 764,526; 819,135; 831,670; 998,004; 1,069,290; 1,092,180; 1,146,789; 1,247,505; 1,274,210; 1,497,006; 1,529,052; 1,638,270; 1,663,340; 1,911,315; 1,984,127; 2,138,580; 2,293,578; 2,495,010; 2,548,420; 2,994,012; 3,276,540; 3,742,515; 3,822,630; 3,968,254; 4,587,156; 4,990,020; 5,733,945; 5,952,381; 7,485,030; 7,645,260; 7,936,508; 9,920,635; 11,467,890; 11,904,762; 13,888,889; 14,970,060; 17,857,143; 19,841,270; 22,935,780; 23,809,524; 27,777,778; 29,761,905; 35,714,286; 39,682,540; 41,666,667; 55,555,556; 59,523,810; 69,444,445; 71,428,572; 83,333,334; 89,285,715; 119,047,620; 125,000,001; 138,888,890; 166,666,668; 178,571,430; 208,333,335; 250,000,002; 277,777,780; 357,142,860; 416,666,670; 500,000,004; 625,000,005; 833,333,340; 1,250,000,010 and 2,500,000,020
out of which 6 prime factors: 2; 3; 5; 7; 109 and 167.
Numbers other than 1 that are not prime factors are composite factors (divisors).
2,500,000,020 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".