What is the prime factorization of 82?

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What is the prime factorization of 82?

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Answer 1 · 2017-03-30T00:01:20

$82 = color(green)(2 xx 41)$

Explanation:

Starting with the smallest prime, $2$
$82 = 2 xx 41$

$41$ is not divisible by $2$ , so try the next smallest prime $3$

...but $41$ is not divisible by $3$ , so try the next smallest prime $5$

...but $41$ is not divisible by $5$ , so try the next smallest prime $7$

...but $41$ is not divisible by $7$
$color(white)("XXX")$ and there is no need to check any further since
$color(white)("XXX")$ if $41$ were divisible by something bigger than $7$
$color(white)("XXX")$ then it would need a factor smaller than $7$
$color(white)("XXX")$ and we have ruled out all such possibilities.

i.e. $41$ is prime

and the prime factors of $82$ can not be reduced further than $2xx41$

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What is the prime factorization of 82?

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