jmc

Let's find the prime factorization of 1512: $1512=2^3\cdot 189=2^3\cdot 3^3\cdot 7$. The only two squares of primes that divide 1512 are $2^2=4$ and $3^2=9$. Therefore, the largest perfect square factor of 1512 is $2^2\cdot 3^2=(2\cdot 3{)}^2=\boxed{36}$.