What is the largest perfect square factor of 1512?
I know that 1512 is divisible by 2, so I can try to factor out powers of 2 until I get an odd number. Dividing by 2 once, I get 756. Dividing by 2 again, I get 378. Dividing by 2 one more time, I get 189. Now 189 is odd, so I can't divide by 2 anymore. I notice that 189 is divisible by 3, so I can try to factor out powers of 3. Dividing by 3 once, I get 63. Dividing by 3 again, I get 21. Dividing by 3 one more time, I get 7. Now 7 is prime, so I can't factor it anymore. I have factored 1512 as 2^3 * 3^3 * 7. To find the largest perfect square factor, I need to use the highest even powers of each prime factor. The highest even power of 2 that I have is 2^2. The highest even power of 3 that I have is 3^2. The highest even power of 7 that I have is 7^0, which is just 1. So the largest perfect square factor is 2^2 * 3^2 * 7^0, which is 36. 