If $N$ is a perfect square and a divisor of $15!$, what is the greatest possible value of $N$?

Question

If $N$ is a perfect square and a divisor of $15!$, what is the greatest possible value of $N$ ? My answer is $$914457600$$ I found it by:

• Noting $15!=13\cdot11\cdot7^2\cdot5^3\cdot2^{11}\cdot3^6$

• Make the biggest perfect square number: $7^2\cdot5^2\cdot2^{10}\cdot3^6=914457600$

Is my answer correct?

Answer 1

Apart from putting the powers of $2$ last to make the order look nicer ($15!=13×11×7^2×5^3×3^6×2^{11}$ and similarly for $N$), the math is correct.