Enter Number 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

Number Factor Pairs Factor Pairs Sum 72 1 x 72 73 72 2 x 36 38 72 3 x 24 27 72 4 x 18 22 72 6 x 12 18 72 8 x 9 17

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

2^{3} x 3^{2}

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

What is the Answer?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

How does the Factorization Calculator work?
Free Factorization Calculator - Given a positive integer, this calculates the following for that number:
1) Factor pairs and prime factorization and prime power decomposition
2) Factors and Proper Factors
3) Aliquot Sum This calculator has 1 input.

What 3 formulas are used for the Factorization Calculator?
Find all pairs that have a product equal to the number you want to factor

For factors in step 1, find the prime factorization for each number

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Formula Dossier
What 7 concepts are covered in the Factorization Calculator?
aliquot sum aliquot sum is the sum of all the factors of a number except the number itself digit Any of the numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) used to construct a number factor a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. factorization power how many times to use the number in a multiplication prime number a natural number greater than 1 that is not a product of two smaller natural numbers. sum the total amount resulting from the addition of two or more numbers, amounts, or items

Example calculations for the Factorization Calculator
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