Show Factorization for 36

Enter Number

Show all factor pairs, prime factorization,

sum of factors (divisors), aliquot sum,

and prime power decomposition of 36

Factor Pair Logic Rules

1) 0 < Factor Pairs ≤ 36

2) The factor pair product = 36

Factor Pairs Table

Number	Factor Pairs	Factor Pairs Sum
36	1 x 36	37
36	2 x 18	20
36	3 x 12	15
36	4 x 9	13
36	6 x 6	12

There are 5 factor pairs of 36

List factors of 36 also known as τ(36)

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

τ(36) = 9

List odd factors of 36

1, 3, 9

List even factors of 36

2, 4, 6, 12, 18, 36

Calculate proper factors of 36

Proper factors are all factors except for the number itself
in this case 36

1, 2, 3, 4, 6, 9, 12, 18

Prime factorization for 36

36 = 2 x 18 <--- 2 is a prime number

Reduce 18 to the product of primes:

18 = 3 x 6 <--- 3 is a prime number

Reduce 6 to the product of primes:

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

Reduce 3 to the product of primes:

Show prime factorization:

2 x 2 x 3 x 3

Prime Power Decomposition

2² x 3²

Show the sum of factors (divisors) for 36

1 + 36 + 2 + 18 + 3 + 12 + 4 + 9 + 6 = 91

Show the aliquot sum:

This is the sum of all the factors except the number

1 + 2 + 18 + 3 + 12 + 4 + 9 + 6 = 55

Common Core State Standards In This Lesson

4.OA.A.4

What is the Answer?

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

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

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