Given the Numbers 728,640 and 971,520, Calculate (Find) All the Common Factors (All the Divisors) of the Two Numbers (and the Prime Factors)

The common factors (divisors) of the numbers 728,640 and 971,520

The common factors (divisors) of the numbers 728,640 and 971,520 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.


728,640 = 26 × 32 × 5 × 11 × 23
728,640 is not a prime number but a composite one.


971,520 = 28 × 3 × 5 × 11 × 23
971,520 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 (728,640; 971,520) = 26 × 3 × 5 × 11 × 23 = 242,880




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
prime factor = 11
22 × 3 = 12
3 × 5 = 15
24 = 16
22 × 5 = 20
2 × 11 = 22
prime factor = 23
23 × 3 = 24
2 × 3 × 5 = 30
25 = 32
3 × 11 = 33
23 × 5 = 40
22 × 11 = 44
2 × 23 = 46
24 × 3 = 48
5 × 11 = 55
22 × 3 × 5 = 60
26 = 64
2 × 3 × 11 = 66
3 × 23 = 69
24 × 5 = 80
23 × 11 = 88
22 × 23 = 92
25 × 3 = 96
2 × 5 × 11 = 110
5 × 23 = 115
23 × 3 × 5 = 120
22 × 3 × 11 = 132
2 × 3 × 23 = 138
25 × 5 = 160
3 × 5 × 11 = 165
24 × 11 = 176
23 × 23 = 184
26 × 3 = 192
22 × 5 × 11 = 220
2 × 5 × 23 = 230
24 × 3 × 5 = 240
11 × 23 = 253
23 × 3 × 11 = 264
22 × 3 × 23 = 276
26 × 5 = 320
2 × 3 × 5 × 11 = 330
3 × 5 × 23 = 345
25 × 11 = 352
24 × 23 = 368
23 × 5 × 11 = 440
22 × 5 × 23 = 460
25 × 3 × 5 = 480
This list continues below...

... This list continues from above
2 × 11 × 23 = 506
24 × 3 × 11 = 528
23 × 3 × 23 = 552
22 × 3 × 5 × 11 = 660
2 × 3 × 5 × 23 = 690
26 × 11 = 704
25 × 23 = 736
3 × 11 × 23 = 759
24 × 5 × 11 = 880
23 × 5 × 23 = 920
26 × 3 × 5 = 960
22 × 11 × 23 = 1,012
25 × 3 × 11 = 1,056
24 × 3 × 23 = 1,104
5 × 11 × 23 = 1,265
23 × 3 × 5 × 11 = 1,320
22 × 3 × 5 × 23 = 1,380
26 × 23 = 1,472
2 × 3 × 11 × 23 = 1,518
25 × 5 × 11 = 1,760
24 × 5 × 23 = 1,840
23 × 11 × 23 = 2,024
26 × 3 × 11 = 2,112
25 × 3 × 23 = 2,208
2 × 5 × 11 × 23 = 2,530
24 × 3 × 5 × 11 = 2,640
23 × 3 × 5 × 23 = 2,760
22 × 3 × 11 × 23 = 3,036
26 × 5 × 11 = 3,520
25 × 5 × 23 = 3,680
3 × 5 × 11 × 23 = 3,795
24 × 11 × 23 = 4,048
26 × 3 × 23 = 4,416
22 × 5 × 11 × 23 = 5,060
25 × 3 × 5 × 11 = 5,280
24 × 3 × 5 × 23 = 5,520
23 × 3 × 11 × 23 = 6,072
26 × 5 × 23 = 7,360
2 × 3 × 5 × 11 × 23 = 7,590
25 × 11 × 23 = 8,096
23 × 5 × 11 × 23 = 10,120
26 × 3 × 5 × 11 = 10,560
25 × 3 × 5 × 23 = 11,040
24 × 3 × 11 × 23 = 12,144
22 × 3 × 5 × 11 × 23 = 15,180
26 × 11 × 23 = 16,192
24 × 5 × 11 × 23 = 20,240
26 × 3 × 5 × 23 = 22,080
25 × 3 × 11 × 23 = 24,288
23 × 3 × 5 × 11 × 23 = 30,360
25 × 5 × 11 × 23 = 40,480
26 × 3 × 11 × 23 = 48,576
24 × 3 × 5 × 11 × 23 = 60,720
26 × 5 × 11 × 23 = 80,960
25 × 3 × 5 × 11 × 23 = 121,440
26 × 3 × 5 × 11 × 23 = 242,880

728,640 and 971,520 have 112 common factors (divisors):
1; 2; 3; 4; 5; 6; 8; 10; 11; 12; 15; 16; 20; 22; 23; 24; 30; 32; 33; 40; 44; 46; 48; 55; 60; 64; 66; 69; 80; 88; 92; 96; 110; 115; 120; 132; 138; 160; 165; 176; 184; 192; 220; 230; 240; 253; 264; 276; 320; 330; 345; 352; 368; 440; 460; 480; 506; 528; 552; 660; 690; 704; 736; 759; 880; 920; 960; 1,012; 1,056; 1,104; 1,265; 1,320; 1,380; 1,472; 1,518; 1,760; 1,840; 2,024; 2,112; 2,208; 2,530; 2,640; 2,760; 3,036; 3,520; 3,680; 3,795; 4,048; 4,416; 5,060; 5,280; 5,520; 6,072; 7,360; 7,590; 8,096; 10,120; 10,560; 11,040; 12,144; 15,180; 16,192; 20,240; 22,080; 24,288; 30,360; 40,480; 48,576; 60,720; 80,960; 121,440 and 242,880
out of which 5 prime factors: 2; 3; 5; 11 and 23

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 728,640 and 971,520? How to calculate them? Mar 29 06:20 UTC (GMT)
What are all the common factors (all the divisors and the prime factors) of the numbers 82 and 0? How to calculate them? Mar 29 06:20 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 36,079,223? How to calculate them? Mar 29 06:20 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 582,988? How to calculate them? Mar 29 06:20 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 257,196? How to calculate them? Mar 29 06:20 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 619,200,000? How to calculate them? Mar 29 06:19 UTC (GMT)
What are all the common factors (all the divisors and the prime factors) of the numbers 18 and 32? How to calculate them? Mar 29 06:19 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 101,778,768? How to calculate them? Mar 29 06:19 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 30,083,038? How to calculate them? Mar 29 06:19 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 294? How to calculate them? Mar 29 06:19 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".