Math CentralQuandaries & Queries


Question from lisa, a parent:

My son has a question which I cannot help him solve. If n is a positive integer such that 5n has 36 positive factors, and 3n has 40 positive factors:
How many positive factors can 15n have? How many values are possible for n?


I'm assuming that you know how many factors an integer has in terms of the number of primes that divide it. Having said that, one way to start is to ask yourself the questions whether or not n has a factor of 3 or of 5 already. If neither what would it say about the number of factors? I think you may find it's impossible. So n has at least a factor of 3 &/or 5. Could it have just one 3 in it? If so n's number of factors would be even and 3n's would be a multiple of 3, but it's not.

I think you need to follow this line of thinking, hope this helps,



About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS