What is the perfect square factor of 80?

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What is the perfect square factor of 80?

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Answer 1 · 2015-06-29T00:05:41

The largest perfect square factor of $80$ $80$ is $16 = 4^{2}$ $16 = 4^2$ ,
but other factors of $80$ $80$ are perfect squares, viz. $4 = 2^{2}$ $4=2^2$ and $1 = 1^{2}$ $1=1^2$

Explanation:

The prime factorisation of $80$ $80$ is $2^{4} \cdot 5$ $2^4 * 5$

Since $5$ $5$ only occurs once, it cannot be a factor of any square factor.

For a factor to be square, it must contain any prime factor an even number of times.

The possibilities are $2^{0} = 1$ $2^0 = 1$ , $2^{2} = 4$ $2^2 = 4$ and $2^{4} = 16$ $2^4 = 16$ .

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What is the perfect square factor of 80?

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