Let $A$ and $B$ be the sets of all positive divisors of 400 and 1000 respectively including 1. Then

Question

Let $A$ and $B$ be the sets of all positive divisors of 400 and 1000 respectively including 1. Then the number of elements in $A \cap B$ is

Professor PC Thomas Classes · Answer

$A \cap B$ represents common divisors, which are divisors of $	ext{gcd}(400, 1000) = 200$. $200 = 2^3 	imes 5^2$. Number of divisors $= 4 	imes 3 = 12$.