Hello could anyone help me prove this Let r s t and v be int

Hello, could anyone help me prove this:

Let r, s, t and v be integers. If gcd(r, s) = t and s divides rv, then s divides tv.

Aside from stating the assumtions I don\'t have a clue what to do next.

Solution

gcd (r,s) = t

that is t is the common factor between the integers r and s

now now s divides rv is true as s and r have a common factor t between them.

now we need to prove that s divides tv

we know that the gcd(r,s) is= t

so t is a factor of both r and s

=> that t we be present within r and s

so as t is a part of both r and s

=> t and r

t and s

are both divisble

=> s divides tv

has been proved.