# What is the prime factorization of 212?

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Bill K. Share
Dec 26, 2017

$212 = {2}^{2} \cdot 53$

#### Explanation:

First, note that $212$ is even and $212 = 2 \cdot 106$. We next note that $106$ is even and $106 = 2 \cdot 53$.

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 $\frac{53}{3} \approx 17.67$ (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 $\frac{53}{7} \approx 7.57$.

Therefore, 53 is prime and the final answer is $212 = {2}^{2} \cdot 53$.

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