Question

If f(ab) = f(a) f(b) for all positive integers a and b, then the largest possible value of f(1) is ___

Answer 1

When a = 1, b = 1
f(1x1) = f(1)f(1)
$\Rightarrow f\left(1\right)=f(1{)}^2$
Also for a = 2, b = 1
f(2x1) = f(2)f(1) = f(1), and this is true for any value, when any of ‘a’ or ‘b’ is is equal to 1.
Hence, largest possible value of f(1) = 1