find the hcf of 4x^2y and 8xy^3

HCF = highest common factor.
The hcf is the biggest factor that EVENLY divides the two terms given.
We see that 4 and 8 are evenly divided by 4.
So, 4 is part of the hcf
I also see x in both terms. We know that x^2 and x can be evenly divided by x. So, x is part of the hcf. The same thing can be said about y.
Answer: 4xy is the hcf.