How do you find the prime factorization of 112?

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How do you find the prime factorization of 112?

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Answer 1 · 2015-02-05T13:05:06

You divide by primes, untill you run out.

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

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

So the complete factorisation:

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

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How do you find the prime factorization of 112?

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