Q: What is special about the factors of a square number?

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Square numbers have an odd number of factors, all others have an even number. In this context, primes can either be considered as having 0 factors (an even number) or 2 factors - 1 and itself, again, an even number.

No, only square numbers have an odd number of factors.

if the factors are equal the the number must be a square so the factor is the square root.

It depends on the number that it is a perfect square of!

If you mean 'prime' factors, then an odd number of them CAN'T produce a perfect square. Consider 3 factors ... A, B, and C. If their product were a perfect square, then AxB=C, which can't be true if C is a prime number. For non-prime factors, an odd number of them may or may not be a perfect square: Three factors = not a square: 2 x 3 x 5 = 30. Three factors = a square: 2 x 3 x 6 = 36.

Related questions

Square numbers have an odd number of factors, all others have an even number. In this context, primes can either be considered as having 0 factors (an even number) or 2 factors - 1 and itself, again, an even number.

A square number has an odd number of factors, but a number with an odd number of factor pairs is nothing special.

Square numbers have an odd number of factors.

The next square number after ten (which is not a square number) is 16. Sixteen has five factors.

All square numbers have an odd number of factors.

A square number will have one factor pair that consists of the same number (the square root). In the list of factors, that number will be written once.

No, only square numbers have an odd number of factors.

Square numbers have an odd number of factors.

Square numbers have an odd number of factors.

Square numbers have an odd number of factors.

A factor of a number, a, is a number, b, that when multipled with another number, c, becomes a. note that both b and c are factors, and a number always has itself and 1 as factors. 0 is special. The factors of 15 are: 1, 3, 5, 15. Only square numbers have odd amount of factors.

A perfect square has an odd number of factors.