math
posted by vincent on .
58. Let GCF (x,y) represent the greatest common factor of x any y. If p is a positive even integer less than 11, for what value of p does GCF (p^2,81) have the greatest value?

I'd make that 6, since 81 = 3^4.
p^2 must have some powers of 3 in it, else GCF(p^2,81) = 1.
GCF(36,81) = 9
9 would be better, but we needed an even integer. 
Is it 4?

hmmm. Is it 4?
Is 4^2 = 36?
Does 4 have 3 as a factor?
Better read what I wrote, and this time pay attention.