Show Factorization for 256

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Show all factor pairs, prime factorization (factor tree), sum of factors (divisors), aliquot sum, and prime power decomposition of 256.

We do this by listing out all pairs of numbers greater than 0 and less than or equal to 256 who have a product equal to 256:
256 = 1 x 256
256 = 2 x 128
256 = 4 x 64
256 = 8 x 32
256 = 16 x 16

There are 5 factor pairs of 256.

List factors of 256
1, 2, 4, 8, 16, 32, 64, 128, 256

List odd factors of 256
1

List even factors of 256
2, 4, 8, 16, 32, 64, 128, 256

Calculate proper factors of 256
Proper factors are all factors except for the number itself, in this case 256
1, 2, 4, 8, 16, 32, 64, 128

Now, show the prime factorization (factor tree) for 256 by expressing it as the product of ALL prime numbers.
256 = 2 x 128 <--- 2 is a prime number

Next step is to reduce 128 to the product of prime numbers:
128 = 2 x 64 <--- 2 is a prime number

Next step is to reduce 64 to the product of 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 x 2 x 2

Show the Prime Power Decomposition (Group Common Terms)
28

Show the sum of factors (divisors) for 256
1 + 256 + 2 + 128 + 4 + 64 + 8 + 32 + 16 = 511

Show the aliquot sum:
The aliquot sum is the sum of all the factors of a number except the number itself
1 + 2 + 128 + 4 + 64 + 8 + 32 + 16 = 255