l Show Factorization for 72

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Show all factor pairs, prime factorization,

sum of factors (divisors), aliquot sum,

and prime power decomposition of 72

Factor Pair Logic Rules

1) 0 < Factor Pairs ≤ 72

2) The factor pair product = 72

Factor Pairs Table

NumberFactor PairsFactor Pairs Sum
721 x 7273
722 x 3638
723 x 2427
724 x 1822
726 x 1218
728 x 917

There are 6 factor pairs of 72

List factors of 72 also known as τ(72)

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

τ(72) = 12

List odd factors of 72

1, 3, 9

List even factors of 72

2, 4, 6, 8, 12, 18, 24, 36, 72

Calculate proper factors of 72

Proper factors are all factors except for the number itself
in this case 72

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36

Prime factorization for 72

72 = 2 x 36 <--- 2 is a prime number

Reduce 36 to the product of primes:

36 = 3 x 12 <--- 3 is a prime number

Reduce 12 to the product of primes:

12 = 2 x 6 <--- 2 is a prime number

Reduce 6 to the product of primes:

6 = 3 x 2 <--- 3 is a prime number

Reduce 2 to the product of primes:

Show prime factorization:

2 x 2 x 2 x 3 x 3

Prime Power Decomposition

23 x 32

Show the sum of factors (divisors) for 72

1 + 72 + 2 + 36 + 3 + 24 + 4 + 18 + 6 + 12 + 8 + 9 = 195

Show the aliquot sum:

This is the sum of all the factors except the number

1 + 2 + 36 + 3 + 24 + 4 + 18 + 6 + 12 + 8 + 9 = 123

Final Answer


1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72