Question

Which is the prime factorization of 86?

Answer 1

`86=2xx43`

Explanation:

First note that `86` ends with an even digit `6` so is itself divisible by `2`:

`86 = 2 xx 43`

You may know that `43` is prime, but let's verify:

• `43` ends with an odd digit, so is not divisible by `2`

• The sum of the digits of `43` is `4+3 = 7`, which is not divisible by `3`, so `43` is not divisible by `3` either.

• The last digit of `43` is not `0` or `5`, so it is not divisible by `5`.

• `43/7 = 6` with remainder `1`

Note that `7^2 = 49 > 43`, so there can be no other prime factors greater than `7` without there being one less than `7` too.

So `43` is prime.