Why does a square number always have an odd amount of factors?

let's ask a related question: why do number that aren't squares always have a even number of factors?

this answer is that the factors of a number comes in pairs. for example, the factors of the number 20 are: 1,2,4,5,10, and 20. Because you can write the number 20 as: 1 x 20, 2 x 10, or 4 x 5

for any number that is not a perfect square ever factor will have a partner that you multiply it by in order to get the number. therefore, each factor has a number and therefore the number of factors are always even.

for a perfect square there will always be a lone factor who doesn't have a partner. the question you have to answer is "why is that", to solve your math problem.

hope this helped the best I can do and it's the best way I know to explain it

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