Given the Numbers 38,319,360 and 42,151,296, Calculate (Find) All the Common Factors (All the Divisors) of the Two Numbers (and the Prime Factors)

The common factors (divisors) of the numbers 38,319,360 and 42,151,296

The common factors (divisors) of the numbers 38,319,360 and 42,151,296 are all the factors of their 'greatest (highest) common factor (divisor)', gcf.

Calculate the greatest (highest) common factor (divisor).
Follow the two steps below.

1. Carry out the prime factorization of the two numbers:

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


38,319,360 = 28 × 3 × 5 × 17 × 587
38,319,360 is not a prime number but a composite one.


42,151,296 = 27 × 3 × 11 × 17 × 587
42,151,296 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.



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

Multiply all the common prime factors, taken by their smallest exponents (the smallest powers).


gcf, hcf, gcd (38,319,360; 42,151,296) = 27 × 3 × 17 × 587 = 3,831,936




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
22 × 3 = 12
24 = 16
prime factor = 17
23 × 3 = 24
25 = 32
2 × 17 = 34
24 × 3 = 48
3 × 17 = 51
26 = 64
22 × 17 = 68
25 × 3 = 96
2 × 3 × 17 = 102
27 = 128
23 × 17 = 136
26 × 3 = 192
22 × 3 × 17 = 204
24 × 17 = 272
27 × 3 = 384
23 × 3 × 17 = 408
25 × 17 = 544
prime factor = 587
24 × 3 × 17 = 816
26 × 17 = 1,088
2 × 587 = 1,174
25 × 3 × 17 = 1,632
3 × 587 = 1,761
This list continues below...

... This list continues from above
27 × 17 = 2,176
22 × 587 = 2,348
26 × 3 × 17 = 3,264
2 × 3 × 587 = 3,522
23 × 587 = 4,696
27 × 3 × 17 = 6,528
22 × 3 × 587 = 7,044
24 × 587 = 9,392
17 × 587 = 9,979
23 × 3 × 587 = 14,088
25 × 587 = 18,784
2 × 17 × 587 = 19,958
24 × 3 × 587 = 28,176
3 × 17 × 587 = 29,937
26 × 587 = 37,568
22 × 17 × 587 = 39,916
25 × 3 × 587 = 56,352
2 × 3 × 17 × 587 = 59,874
27 × 587 = 75,136
23 × 17 × 587 = 79,832
26 × 3 × 587 = 112,704
22 × 3 × 17 × 587 = 119,748
24 × 17 × 587 = 159,664
27 × 3 × 587 = 225,408
23 × 3 × 17 × 587 = 239,496
25 × 17 × 587 = 319,328
24 × 3 × 17 × 587 = 478,992
26 × 17 × 587 = 638,656
25 × 3 × 17 × 587 = 957,984
27 × 17 × 587 = 1,277,312
26 × 3 × 17 × 587 = 1,915,968
27 × 3 × 17 × 587 = 3,831,936

38,319,360 and 42,151,296 have 64 common factors (divisors):
1; 2; 3; 4; 6; 8; 12; 16; 17; 24; 32; 34; 48; 51; 64; 68; 96; 102; 128; 136; 192; 204; 272; 384; 408; 544; 587; 816; 1,088; 1,174; 1,632; 1,761; 2,176; 2,348; 3,264; 3,522; 4,696; 6,528; 7,044; 9,392; 9,979; 14,088; 18,784; 19,958; 28,176; 29,937; 37,568; 39,916; 56,352; 59,874; 75,136; 79,832; 112,704; 119,748; 159,664; 225,408; 239,496; 319,328; 478,992; 638,656; 957,984; 1,277,312; 1,915,968 and 3,831,936
out of which 4 prime factors: 2; 3; 17 and 587

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

What are all the common factors (all the divisors and the prime factors) of the numbers 38,319,360 and 42,151,296? How to calculate them? Mar 28 08:27 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 1,977,956? How to calculate them? Mar 28 08:27 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 59,956,875? How to calculate them? Mar 28 08:27 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 1,590,001? How to calculate them? Mar 28 08:27 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 20,691,968? How to calculate them? Mar 28 08:27 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 200,704,000? How to calculate them? Mar 28 08:27 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 55,825? How to calculate them? Mar 28 08:27 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 181,992? How to calculate them? Mar 28 08:27 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 2,104,899? How to calculate them? Mar 28 08:27 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 208,424,796? How to calculate them? Mar 28 08:27 UTC (GMT)
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".