Question

How many positive factors of the number 36,000,000 are not perfect squares?

Answer 1

\[6^{2}\times10^{6}\]

Answer 2

find the prime factorization first

Answer 3

\[(2*2*3*3)*(10*10*10*10*10*10)?\]? not sure

Answer 4

10 can also be broken down as 5 * 2

Answer 5

yeah, so \[2^{8}*3^{3}*5^{6}\]

Answer 6

In order for the number to be perfect factors, it is in the form: \[2^{2n} * 3^{2m} *5^{2p}\]

Answer 7

okay.

Answer 8

i don't fully understand... the form above?

Answer 9

for 2, n can be equal to 0, 1, 2, 3, 4; 5 choices

for 3, m can be equal to 0, 1; 2 choices

for 5, p can be equal to 0, 1, 2, 3; 4 choices

Answer 10

number of perfect squares is 5 * 2 * 4 = 40

Answer 11

do you know the answer?

Answer 12

9 * 4 * 7 = number of factors = 252

Answer 13

number of non-perfect squares' factors = 252 - 40 = 212

Answer 14

I had no clue that was how it was supposed to be done... i wish i was able to give more than a medal here, but thank you so much for your help :)

Answer 15

np