What is 8+16 when you are doing a prime fractorization

"Prime Factorization" is finding which prime numbers multiply together to make the original number.
∴ 8 = 2 * 2 * 2 
And  16 = 2 * 2 * 2 * 2

∴ 8 + 16 = 2 * 2 * 2 + 2 * 2 * 2 * 2   ⇒⇒⇒ taking ( 2 * 2 * 2) as a common

∴ 8 + 16 = (2 * 2 * 2) ( 1 + 2 )
               = 2 * 2 * 2 * 3 
               = 24

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