Proving divisibility if and only if also divisible by factors

Question

I need to prove, that $10|a$ if and only if $5|a$ and $2|a$. Divisibility properties say, that if $a|b$ then b is also divisible by $a$-s factors. I think I need to show that $10|a$ and then that it is also divisible by it's factors. Am I going the right way?

Answer 1

If $10 \mid a$, then $a = 10x$ for some $x$. Notice, we can also write $a = 2 \cdot 5 \cdot x$. Now, what does this tell you?