# Greatest common divisor of a, 2b

Let $$a$$ and $$b$$ be positive integers where $$a$$ is even and such that $$\gcd(2a, 2b) = 70$$. Find $$\gcd(a, 2b)$$.

If $$\gcd(2a, 2b) = 70$$ then we know that $$2a = 70m$$ and $$2b = 70n$$ for some integers $$m, n$$ (where $$\gcd(m, n) = 1$$), which means that $$a = 35m$$. But, since $$a$$ is even, $$a = 70k$$ for some integer $$k$$ (where $$m = 2k$$).