Question 427325
It is the same problem as 
"What is the greatest common factor of
30 and 48?"
3 divides both of them, but so does 6,
so that's the answer.
Looking at {{{ 8a*b^3}}} and {{{2a*b^2}}},
I see that {{{2}}} is a common factor, so is
{{{a}}} and {{{b^2}}}. Note that {{{b^3}}} will
not divide into {{{2a*b^2}}} evenly.
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{{{2a*b2}}} is the common factor because
{{{2a*b^2 / (2a*b^2) = 1}}}
and
{{{8a*b^3 / (2a*b^2) = 4b}}}
Note that there is no remainder in the divisions.