Divisibility of integer numbers

Question

If we have two integers $a$ and $b$ such that $a = \frac{5b}{6}$, is $a$ divisible by $5$?

If so, why is that?

I don't see it.

Answer 1

If $a$ is an integer then $b = 6k, k\in \mathbb{Z}$ so $$a = 5k \Rightarrow a \equiv 0 \pmod{5}$$

Answer 2

If $a$ is an integer, then it is obvious that $6$ divides $5b$ or more specifically $b$.

Hence we can say that, $b=6k$ for some integer $k$.

So $a=5k$

Thus we can conclude that $5$ divides $a$, since $5$ divides $5$.

Answer 3

No prime factorisation is really required here: we have $5b=6a$,so $5$ divides $6a$. Now $5$ is prime, hence by Euclid's lemma, it must divide one of the factors. As it does not divide $6$, it must divide $a$.