# How do you find the prime factorization of 112?

Feb 5, 2015

You divide by primes, untill you run out.

$112$ is even: $112 / 2 = 56 \to 112 = \left(2 \cdot 56\right)$
Still even: $56 / 2 = 28 \to 112 = 2 \cdot \left(2 \cdot 28\right)$
And again: $28 / 2 = 14 \to 112 = 2 \cdot 2 \cdot \left(2 \cdot 14\right)$
And again: $14 / 2 = 7 \to 112 = 2 \cdot 2 \cdot 2 \cdot \left(2 \cdot 7\right)$
(brackets are only for clarification)

$7$ is a prime (try if you like)

So the complete factorisation:

$112 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 7 = {2}^{4} \cdot 7$