Xiao's teacher asked him to rewrite the sum 60+90 as the product of the gcf of the two numbers and a sum. xiao's wrote 3(20 + 30). what mistake did xiao make? how should he have written the sum?

His answer works ... it gives 150, which is the same as (60 + 90) ... but he didn't deliver exactly what the problem asked for.

It asked for the GCF to be outside the parentheses, and he put  '3'  there.

'3'  is certainly one common factor of 60 and 90, but it's far from being the
greatest one. 

The GCF  of 60 and 90 is actually  30 .  So the absolutely positively technically correct response to the instructions in the problem would be  30(2 + 3).