How many factors of 900 have exactly 18 factors
WHAT I DID (If I got it incorrect tell me what I got wrong)
Prime factorize 900..?
3^2 * 2^2 * 5^2
You find the number of factors of 900 by taking the exponents, adding one to each, and multiplying them out.
3 * 3 * 3 = 27. 900 has 27 factors..
We can apply the same rule to find the numbers that have 18 factors by working backward.
We prime factor 18.
3 * 3 * 2
So it must be in the form:
x^2 * y^2 * z
Values of x, y, z, must be subbed in with 3, 2, 5.
We find the number of ways that can be arranged. So its, just 3!
OMG I am so scared right now I want to do good on the AMC 8. I have like anxiety issues or something because MY BRAIN IS SCREWED up and my HEART is EXPLODING
I know what I did wrong
Oh ok, I know what I did wrong.
Basically I got to a certain point where 2, 3, 5, can be substituted in here:
Then, I find all the possible values, and count them.
I thought it was just 3!, but if you calculated it out, it actually is 3.