# 123,225,144 and 0: Calculate all the common factors (divisors) of the two numbers (and the prime factors)

## The common factors (divisors) of the numbers 123,225,144 and 0 are all the factors of their 'greatest (highest) common factor (divisor)'.

### The list of factors (divisors):

neither prime nor composite = 1
prime factor = 2
prime factor = 3
22 = 4
2 × 3 = 6
prime factor = 7
23 = 8
22 × 3 = 12
2 × 7 = 14
3 × 7 = 21
23 × 3 = 24
22 × 7 = 28
2 × 3 × 7 = 42
23 × 7 = 56
22 × 3 × 7 = 84
prime factor = 113
23 × 3 × 7 = 168
2 × 113 = 226
3 × 113 = 339
22 × 113 = 452
2 × 3 × 113 = 678
7 × 113 = 791
23 × 113 = 904
22 × 3 × 113 = 1,356
2 × 7 × 113 = 1,582
3 × 7 × 113 = 2,373
23 × 3 × 113 = 2,712
22 × 7 × 113 = 3,164
2 × 3 × 7 × 113 = 4,746
23 × 7 × 113 = 6,328
prime factor = 6,491
22 × 3 × 7 × 113 = 9,492
This list continues below...

... This list continues from above
2 × 6,491 = 12,982
23 × 3 × 7 × 113 = 18,984
3 × 6,491 = 19,473
22 × 6,491 = 25,964
2 × 3 × 6,491 = 38,946
7 × 6,491 = 45,437
23 × 6,491 = 51,928
22 × 3 × 6,491 = 77,892
2 × 7 × 6,491 = 90,874
3 × 7 × 6,491 = 136,311
23 × 3 × 6,491 = 155,784
22 × 7 × 6,491 = 181,748
2 × 3 × 7 × 6,491 = 272,622
23 × 7 × 6,491 = 363,496
22 × 3 × 7 × 6,491 = 545,244
113 × 6,491 = 733,483
23 × 3 × 7 × 6,491 = 1,090,488
2 × 113 × 6,491 = 1,466,966
3 × 113 × 6,491 = 2,200,449
22 × 113 × 6,491 = 2,933,932
2 × 3 × 113 × 6,491 = 4,400,898
7 × 113 × 6,491 = 5,134,381
23 × 113 × 6,491 = 5,867,864
22 × 3 × 113 × 6,491 = 8,801,796
2 × 7 × 113 × 6,491 = 10,268,762
3 × 7 × 113 × 6,491 = 15,403,143
23 × 3 × 113 × 6,491 = 17,603,592
22 × 7 × 113 × 6,491 = 20,537,524
2 × 3 × 7 × 113 × 6,491 = 30,806,286
23 × 7 × 113 × 6,491 = 41,075,048
22 × 3 × 7 × 113 × 6,491 = 61,612,572
23 × 3 × 7 × 113 × 6,491 = 123,225,144

## The latest 5 sets of calculated factors (divisors): of one number or the common factors of two numbers

 The common factors (divisors) of 123,225,144 and 0 = ? Jul 05 22:38 UTC (GMT) The common factors (divisors) of 1,694,769,231 and 0 = ? Jul 05 22:38 UTC (GMT) The common factors (divisors) of 8,352,000 and 0 = ? Jul 05 22:38 UTC (GMT) The common factors (divisors) of 3,919,384 and 0 = ? Jul 05 22:38 UTC (GMT) The common factors (divisors) of 888,671,876 and 0 = ? Jul 05 22:38 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".