Same number of factors
Number Theory
Level
2
Ben and Clad has their own favourite positive integer.
It is know that both positive integers have the same number of factors.
What can we say about Ben's and Clad's favourite positive integers?
They must be the same
They can be different
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
If Ben and Clad both have primes as their favorite integers, then those integers will each have two factors, regardless of which primes they choose.
In general, two integers will have the same number of factors if they have the same number of prime factors (with the same multiplicities), regardless of what those prime factors are.