The sum of 2 positive integers is 2310. Show that their product is not divisible by 2310.

Question

I'm not sure how to start. Is 2310 some special number?

Answer 1

$$a + b = N$$

Let $N\mid a\cdot b$. If $p$ is some prime such that $p\mid N$, then both $a$ and $b$ are definitely divisible by $p$.

$2310$ is made up of $5$ different primes. So, if $N\mid a, b$, then both $a$ and $b$ are divisible by $N$. So, $N = a + b \ge 2N$. Contradition.