Given the Numbers 761,600 and 837,760, Calculate (Find) All the Common Factors (All the Divisors) of the Two Numbers (and the Prime Factors)

The common factors (divisors) of the numbers 761,600 and 837,760

The common factors (divisors) of the numbers 761,600 and 837,760 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.


761,600 = 28 × 52 × 7 × 17
761,600 is not a prime number but a composite one.


837,760 = 27 × 5 × 7 × 11 × 17
837,760 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 (761,600; 837,760) = 27 × 5 × 7 × 17 = 76,160




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
22 = 4
prime factor = 5
prime factor = 7
23 = 8
2 × 5 = 10
2 × 7 = 14
24 = 16
prime factor = 17
22 × 5 = 20
22 × 7 = 28
25 = 32
2 × 17 = 34
5 × 7 = 35
23 × 5 = 40
23 × 7 = 56
26 = 64
22 × 17 = 68
2 × 5 × 7 = 70
24 × 5 = 80
5 × 17 = 85
24 × 7 = 112
7 × 17 = 119
27 = 128
23 × 17 = 136
22 × 5 × 7 = 140
25 × 5 = 160
2 × 5 × 17 = 170
25 × 7 = 224
2 × 7 × 17 = 238
24 × 17 = 272
This list continues below...

... This list continues from above
23 × 5 × 7 = 280
26 × 5 = 320
22 × 5 × 17 = 340
26 × 7 = 448
22 × 7 × 17 = 476
25 × 17 = 544
24 × 5 × 7 = 560
5 × 7 × 17 = 595
27 × 5 = 640
23 × 5 × 17 = 680
27 × 7 = 896
23 × 7 × 17 = 952
26 × 17 = 1,088
25 × 5 × 7 = 1,120
2 × 5 × 7 × 17 = 1,190
24 × 5 × 17 = 1,360
24 × 7 × 17 = 1,904
27 × 17 = 2,176
26 × 5 × 7 = 2,240
22 × 5 × 7 × 17 = 2,380
25 × 5 × 17 = 2,720
25 × 7 × 17 = 3,808
27 × 5 × 7 = 4,480
23 × 5 × 7 × 17 = 4,760
26 × 5 × 17 = 5,440
26 × 7 × 17 = 7,616
24 × 5 × 7 × 17 = 9,520
27 × 5 × 17 = 10,880
27 × 7 × 17 = 15,232
25 × 5 × 7 × 17 = 19,040
26 × 5 × 7 × 17 = 38,080
27 × 5 × 7 × 17 = 76,160

761,600 and 837,760 have 64 common factors (divisors):
1; 2; 4; 5; 7; 8; 10; 14; 16; 17; 20; 28; 32; 34; 35; 40; 56; 64; 68; 70; 80; 85; 112; 119; 128; 136; 140; 160; 170; 224; 238; 272; 280; 320; 340; 448; 476; 544; 560; 595; 640; 680; 896; 952; 1,088; 1,120; 1,190; 1,360; 1,904; 2,176; 2,240; 2,380; 2,720; 3,808; 4,480; 4,760; 5,440; 7,616; 9,520; 10,880; 15,232; 19,040; 38,080 and 76,160
out of which 4 prime factors: 2; 5; 7 and 17

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".