Given the Numbers 616,032 and 0, Calculate (Find) All the Common Factors (All the Divisors) of the Two Numbers (and the Prime Factors)

The common factors (divisors) of the numbers 616,032 and 0

The common factors (divisors) of the numbers 616,032 and 0 are all the factors of their 'greatest (highest) common factor (divisor)', gcf.

Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd:

Zero is divisible by any number other than zero (there is no remainder when dividing zero by these numbers).

The greatest factor (divisor) of the number 616,032 is the number itself.


⇒ gcf, hcf, gcd (616,032; 0) = 616,032




To find all the factors (all the divisors) of the 'gcf', we need its prime factorization (to decompose it into prime factors).

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


616,032 = 25 × 33 × 23 × 31
616,032 is not a prime number but a composite one.



* Prime number: a natural number that is divisible only by 1 and itself. A prime number has exactly two factors: 1 and itself.
* Composite number: a natural number that has at least one other factor than 1 and itself.



Multiply the prime factors of the 'gcf':

Multiply the prime factors involved in the prime factorization of the GCF in all their unique combinations, that give different results.


Also consider the exponents of the prime factors (example: 32 = 3 × 3 = 9).


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
23 = 8
32 = 9
22 × 3 = 12
24 = 16
2 × 32 = 18
prime factor = 23
23 × 3 = 24
33 = 27
prime factor = 31
25 = 32
22 × 32 = 36
2 × 23 = 46
24 × 3 = 48
2 × 33 = 54
2 × 31 = 62
3 × 23 = 69
23 × 32 = 72
22 × 23 = 92
3 × 31 = 93
25 × 3 = 96
22 × 33 = 108
22 × 31 = 124
2 × 3 × 23 = 138
24 × 32 = 144
23 × 23 = 184
2 × 3 × 31 = 186
32 × 23 = 207
23 × 33 = 216
23 × 31 = 248
22 × 3 × 23 = 276
32 × 31 = 279
25 × 32 = 288
24 × 23 = 368
22 × 3 × 31 = 372
2 × 32 × 23 = 414
24 × 33 = 432
24 × 31 = 496
23 × 3 × 23 = 552
2 × 32 × 31 = 558
33 × 23 = 621
23 × 31 = 713
25 × 23 = 736
23 × 3 × 31 = 744
This list continues below...

... This list continues from above
22 × 32 × 23 = 828
33 × 31 = 837
25 × 33 = 864
25 × 31 = 992
24 × 3 × 23 = 1,104
22 × 32 × 31 = 1,116
2 × 33 × 23 = 1,242
2 × 23 × 31 = 1,426
24 × 3 × 31 = 1,488
23 × 32 × 23 = 1,656
2 × 33 × 31 = 1,674
3 × 23 × 31 = 2,139
25 × 3 × 23 = 2,208
23 × 32 × 31 = 2,232
22 × 33 × 23 = 2,484
22 × 23 × 31 = 2,852
25 × 3 × 31 = 2,976
24 × 32 × 23 = 3,312
22 × 33 × 31 = 3,348
2 × 3 × 23 × 31 = 4,278
24 × 32 × 31 = 4,464
23 × 33 × 23 = 4,968
23 × 23 × 31 = 5,704
32 × 23 × 31 = 6,417
25 × 32 × 23 = 6,624
23 × 33 × 31 = 6,696
22 × 3 × 23 × 31 = 8,556
25 × 32 × 31 = 8,928
24 × 33 × 23 = 9,936
24 × 23 × 31 = 11,408
2 × 32 × 23 × 31 = 12,834
24 × 33 × 31 = 13,392
23 × 3 × 23 × 31 = 17,112
33 × 23 × 31 = 19,251
25 × 33 × 23 = 19,872
25 × 23 × 31 = 22,816
22 × 32 × 23 × 31 = 25,668
25 × 33 × 31 = 26,784
24 × 3 × 23 × 31 = 34,224
2 × 33 × 23 × 31 = 38,502
23 × 32 × 23 × 31 = 51,336
25 × 3 × 23 × 31 = 68,448
22 × 33 × 23 × 31 = 77,004
24 × 32 × 23 × 31 = 102,672
23 × 33 × 23 × 31 = 154,008
25 × 32 × 23 × 31 = 205,344
24 × 33 × 23 × 31 = 308,016
25 × 33 × 23 × 31 = 616,032

616,032 and 0 have 96 common factors (divisors):
1; 2; 3; 4; 6; 8; 9; 12; 16; 18; 23; 24; 27; 31; 32; 36; 46; 48; 54; 62; 69; 72; 92; 93; 96; 108; 124; 138; 144; 184; 186; 207; 216; 248; 276; 279; 288; 368; 372; 414; 432; 496; 552; 558; 621; 713; 736; 744; 828; 837; 864; 992; 1,104; 1,116; 1,242; 1,426; 1,488; 1,656; 1,674; 2,139; 2,208; 2,232; 2,484; 2,852; 2,976; 3,312; 3,348; 4,278; 4,464; 4,968; 5,704; 6,417; 6,624; 6,696; 8,556; 8,928; 9,936; 11,408; 12,834; 13,392; 17,112; 19,251; 19,872; 22,816; 25,668; 26,784; 34,224; 38,502; 51,336; 68,448; 77,004; 102,672; 154,008; 205,344; 308,016 and 616,032
out of which 4 prime factors: 2; 3; 23 and 31

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".