Question

What is the perfect square factor of 80?

Answer 1

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 * 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`.