SOLUTION: What type of numbers have an odd number of factors?

Question 713719: What type of numbers have an odd number of factors?
Answer by Simnepi(216) (Show Source): You can put this solution on YOUR website!
Most numbers have factors which come in pairs. These pairs multiply together to make the number.
i.e. factors of 12 are
1 and 12
2 and 6
3 and 4
The product of these factor pairs is 12.
as an ordered list these factors are written
1, 2, 3, 4, 6, 12. we have an even number of factors.
now lets look at some other numbers, 36 for instance.
Factors of 36 are
1 and 36
2 and 18
3 and 12
4 and 9
6 and 6
because 36 is a square number it has that repeated factor of 6.
as an ordered list we have
1, 2, 3, 4, 6, 9, 12, 18, 36.
Because of the repeated factor which we only write once this number has an odd number of factors.
This occurs in all square numbers.
So your answer is ...
square numbers!
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