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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.
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∙ 11y ago
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Can an odd number have odd numbers of factors?
Yes. Square numbers have an odd number of factors. 49 has three factors.
What is another name for an odd number of factors?
Square numbers have an odd number of factors.
What number has an odd number for a factor?
All odd numbers have odd factors.
Is the number of factors of any square number odd or even?
Odd.
Do odd numbers have a odd or even number of factors?
The number of factors can be either even or odd.
Odd number of factors?
Square numbers have an odd number of factors.
What kind of factors have an odd number of factors?
Square numbers have an odd number of factors.
Can an odd number have odd numbers of factors?
Yes. Square numbers have an odd number of factors. 49 has three factors.
Can a number have an odd number of factors?
Yes, quare numbers have an odd number of factors.
What is a number that has an odd number of factors?
if a number has an odd number of factors it would be a perfect square
What is a number that has odd number of factors?
if a number has an odd number of factors it would be a perfect square
Numbers that have an odd number of factors?
Square numbers have an odd number of factors.
Odd number factors?
Perfect squares are numbers with an odd number of factors.
What is the word for an odd number of factors?
Square numbers have an odd number of factors.
What has an odd number of factors?
Squares have an odd number of factors.
What factors are odd?
Square numbers have an odd number of factors, but beyond that, any odd number can be a factor.
What is a number has an odd number of factors?
An even power. Square numbers have an odd number of factors.
