If $10|abc$, prove that either $10|ab$, $10|bc$, or $10|ac$.

Question

Given three integers $a$, $b$, and $c$ how do I prove that if $10|abc$, it follows that either $10|ab$, $10|bc$, or $10|ac$?

I do not get much further than writing out $abc=10\cdot r$, where $r$ is some integer.

Answer 1

if $10|abc$ then 2 and 5 must be a factor of a,b or c. Thus at least one of ab, bc or ac will have 10 as a factor.

For example if a has 2 as a factor and b has 5 as a factor then 10|ab or if c has 2 and 5 as a factor then 10|ac or 10|bc