We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

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!

So 6?




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

 Nov 15, 2019
edited by CalculatorUser  Nov 15, 2019

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.

 Nov 15, 2019

8 Online Users