What is the prime factorization of 212?

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Bill K. Share
Dec 26, 2017

Answer:

#212=2^2 * 53#

Explanation:

First, note that #212# is even and #212=2*106#. We next note that #106# is even and #106=2*53#.

The number #53# is odd, but is it prime? You can test this by seeing if it's divisible by any prime numbers between #2# and #sqrt(53)approx 7.28#.

We already know #53# is not divisible by 2 since it's not even. It's not divisible by 3 since #53/3 approx 17.67# (also its digits add up to 8, which is not divisible by 3). It's not divisible by 5 since it does not end in a 0 or a 5. And it's not divisible by 7 since #53/7 approx 7.57#.

Therefore, 53 is prime and the final answer is #212=2^2 * 53#.

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