What is the perfect square factor of 80?

1 Answer
Jun 29, 2015

Answer:

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#.