What is the perfect square factor of 80?

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##

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##.