LCM, multiple, factors

Question

Sue found the product of the first six multiples of three.

3x6x9x12x15x18 = 524880

How many factors of 524880 are the square of an integer greater than 1?

Answer 1

There seems to be some misunderstanding of what the problem is asking.

So, we have 3 x 6 x 9 x 12 x 15 x 18 = 524,880

If we break that all down...

3 x 3 x 2 x 3 x 3 x 3 x 2 x 2 x 3 x 5 x 3 x 2 x 3

Put that all in order...

2⁴ x 3⁸ x 5

4 twice

16

4 x 9 = 36 twice

4 x 81 = 324 twice

4 x 6561 = 26,244

16 x 9 = 144

16 x 81 = 1296

16 x 6561 = 104,976

I'm out of time to find the rest, but I bet you can!

Answer 2

The prime factorization of 524880 is 2^4 * 3^8 * 5.

The largest factor that is also a square is 104976, which is 324 squared.