answersLogoWhite

0

Perfect squares have an odd number of factors.

If f is a factor of N, then so is N/f. (For example, 3 is a factor of 30, and so is 10). Thus, it seems factors come in pairs, and there should always be an even number of them. But if f = N/f, then these two factors are the same, resulting in an odd number of factors. For example, 3 is a factor of 9, and it's "mate" is also 3.

So for the numbers with an odd number of factors, there is some f where f=N/f. Multiplying both sides by f, we have f^2 = N. So this happens when N is a perfect square.

User Avatar

Wiki User

12y ago

Still curious? Ask our experts.

Chat with our AI personalities

BlakeBlake
As your older brother, I've been where you are—maybe not exactly, but close enough.
Chat with Blake
ProfessorProfessor
I will give you the most educated answer.
Chat with Professor
LaoLao
The path is yours to walk; I am only here to hold up a mirror.
Chat with Lao

Add your answer:

Earn +20 pts
Q: What is an odd number of factors?
Write your answer...
Submit
Still have questions?
magnify glass
imp