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.

1, 2, 4, 8, 16, 32, 64, 128, 256

1

2, 4, 8, 16, 32, 64, 128, 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:

1 + 256 + 2 + 128 + 4 + 64 + 8 + 32 + 16 =

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 =