# What is the perfect square factor of 80?

Jun 29, 2015

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

#### Explanation:

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

Since $5$ 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 ${2}^{0} = 1$, ${2}^{2} = 4$ and ${2}^{4} = 16$.