One way to I solve this is by listing all the ways it can be multiplied by:
72: 1*72, 2*36, 3*24, 4*18, 6*12, 8*9.
80: 1*80, 2*40, 4*20, 5*16, 8*10.
Group the factors that they have in common.
Which are 1, 2, 4, and 8.
After that, find the greatest common factor that they both share.
Answer: 8