# Factorization Calculator

<-- Enter Number

Show all factor pairs, prime factorization (factor tree), sum of factors (divisors), aliquot sum, and prime power decomposition of 64.

We do this by listing out all pairs of numbers greater than 0 and less than or equal to 64 who have a product equal to 64:
64 = 1 x 64
64 = 2 x 32
64 = 4 x 16
64 = 8 x 8

There are 4 factor pairs of 64.

List factors of 64
1, 2, 4, 8, 16, 32, 64

List odd factors of 64
1

List even factors of 64
2, 4, 8, 16, 32, 64

Calculate proper factors of 64
Proper factors are all factors except for the number itself, in this case 64
1, 2, 4, 8, 16, 32

Now, show the prime factorization (factor tree) for 64 by expressing it as the product of ALL prime numbers.
64 = 2 x 32 <--- 2 is a prime number

Next step is to reduce 32 to the product of prime numbers:
32 = 2 x 16 <--- 2 is a prime number

Next step is to reduce 16 to the product of prime numbers:
16 = 2 x 8 <--- 2 is a prime number

Next step is to reduce 8 to the product of prime numbers:
8 = 2 x 4 <--- 2 is a prime number

Next step is to reduce 4 to the product of prime numbers:
4 = 2 x 2 <--- 2 is a prime number

Next step is to reduce 2 to the product of prime numbers:
Our prime factorization (factor tree) is as follows:
2 x 2 x 2 x 2 x 2 x 2

Show the Prime Power Decomposition (Group Common Terms)
26

Show the sum of factors (divisors) for 64
1 + 64 + 2 + 32 + 4 + 16 + 8 = 127

Show the aliquot sum:
The aliquot sum is the sum of all the factors of a number except the number itself
1 + 2 + 32 + 4 + 16 + 8 = 63