Given the Numbers 857,280 and 3,857,760, Calculate (Find) All the Common Factors (All the Divisors) of the Two Numbers (and the Prime Factors)

The common factors (divisors) of the numbers 857,280 and 3,857,760

The common factors (divisors) of the numbers 857,280 and 3,857,760 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.


857,280 = 26 × 3 × 5 × 19 × 47
857,280 is not a prime number but a composite one.


3,857,760 = 25 × 33 × 5 × 19 × 47
3,857,760 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 (857,280; 3,857,760) = 25 × 3 × 5 × 19 × 47 = 428,640




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
prime factor = 5
2 × 3 = 6
23 = 8
2 × 5 = 10
22 × 3 = 12
3 × 5 = 15
24 = 16
prime factor = 19
22 × 5 = 20
23 × 3 = 24
2 × 3 × 5 = 30
25 = 32
2 × 19 = 38
23 × 5 = 40
prime factor = 47
24 × 3 = 48
3 × 19 = 57
22 × 3 × 5 = 60
22 × 19 = 76
24 × 5 = 80
2 × 47 = 94
5 × 19 = 95
25 × 3 = 96
2 × 3 × 19 = 114
23 × 3 × 5 = 120
3 × 47 = 141
23 × 19 = 152
25 × 5 = 160
22 × 47 = 188
2 × 5 × 19 = 190
22 × 3 × 19 = 228
5 × 47 = 235
24 × 3 × 5 = 240
2 × 3 × 47 = 282
3 × 5 × 19 = 285
24 × 19 = 304
23 × 47 = 376
22 × 5 × 19 = 380
23 × 3 × 19 = 456
2 × 5 × 47 = 470
25 × 3 × 5 = 480
22 × 3 × 47 = 564
2 × 3 × 5 × 19 = 570
25 × 19 = 608
This list continues below...

... This list continues from above
3 × 5 × 47 = 705
24 × 47 = 752
23 × 5 × 19 = 760
19 × 47 = 893
24 × 3 × 19 = 912
22 × 5 × 47 = 940
23 × 3 × 47 = 1,128
22 × 3 × 5 × 19 = 1,140
2 × 3 × 5 × 47 = 1,410
25 × 47 = 1,504
24 × 5 × 19 = 1,520
2 × 19 × 47 = 1,786
25 × 3 × 19 = 1,824
23 × 5 × 47 = 1,880
24 × 3 × 47 = 2,256
23 × 3 × 5 × 19 = 2,280
3 × 19 × 47 = 2,679
22 × 3 × 5 × 47 = 2,820
25 × 5 × 19 = 3,040
22 × 19 × 47 = 3,572
24 × 5 × 47 = 3,760
5 × 19 × 47 = 4,465
25 × 3 × 47 = 4,512
24 × 3 × 5 × 19 = 4,560
2 × 3 × 19 × 47 = 5,358
23 × 3 × 5 × 47 = 5,640
23 × 19 × 47 = 7,144
25 × 5 × 47 = 7,520
2 × 5 × 19 × 47 = 8,930
25 × 3 × 5 × 19 = 9,120
22 × 3 × 19 × 47 = 10,716
24 × 3 × 5 × 47 = 11,280
3 × 5 × 19 × 47 = 13,395
24 × 19 × 47 = 14,288
22 × 5 × 19 × 47 = 17,860
23 × 3 × 19 × 47 = 21,432
25 × 3 × 5 × 47 = 22,560
2 × 3 × 5 × 19 × 47 = 26,790
25 × 19 × 47 = 28,576
23 × 5 × 19 × 47 = 35,720
24 × 3 × 19 × 47 = 42,864
22 × 3 × 5 × 19 × 47 = 53,580
24 × 5 × 19 × 47 = 71,440
25 × 3 × 19 × 47 = 85,728
23 × 3 × 5 × 19 × 47 = 107,160
25 × 5 × 19 × 47 = 142,880
24 × 3 × 5 × 19 × 47 = 214,320
25 × 3 × 5 × 19 × 47 = 428,640

857,280 and 3,857,760 have 96 common factors (divisors):
1; 2; 3; 4; 5; 6; 8; 10; 12; 15; 16; 19; 20; 24; 30; 32; 38; 40; 47; 48; 57; 60; 76; 80; 94; 95; 96; 114; 120; 141; 152; 160; 188; 190; 228; 235; 240; 282; 285; 304; 376; 380; 456; 470; 480; 564; 570; 608; 705; 752; 760; 893; 912; 940; 1,128; 1,140; 1,410; 1,504; 1,520; 1,786; 1,824; 1,880; 2,256; 2,280; 2,679; 2,820; 3,040; 3,572; 3,760; 4,465; 4,512; 4,560; 5,358; 5,640; 7,144; 7,520; 8,930; 9,120; 10,716; 11,280; 13,395; 14,288; 17,860; 21,432; 22,560; 26,790; 28,576; 35,720; 42,864; 53,580; 71,440; 85,728; 107,160; 142,880; 214,320 and 428,640
out of which 5 prime factors: 2; 3; 5; 19 and 47

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.

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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".