Question

What is the prime factorization of 82?

Answer 1

`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`