What is the greatest commong factor

whats the gcf of 5y and yz?

a factor is any quantity that can "go into" (is a divisor of) a larger or equal quantity or whatever quantity is being divided (the dividend)

Greatest Common Factor (abbrev. GCF) is simply the largest of mutual factors.

So
12 and 6

12 has divisors or factors of 1,2,3,4,6 and 12
6 has divisors or factors of 1,2,3, and 6

the greatest common factor is now simple you just look for 1)numbers that appear in both dividends (1,2,3, and 6) and now 2)select the largest of those numbers, in this case 6.

With your original problem the dividends are 5y and yz
the divisors (or factors ) of 5y are 5 and y.
the divisors (or factors ) of yz are y and z.

using hte same 1)identify mutual factors and 2)select the largest one method described above, we see that there exists only one common factor (y) and that, thus is the 1 common factor and the largest (only) factor so y is the GCF of 5y and yz.

answer prob way longer than needed to be but thought extra explanation might help comprehension of and acquiring GCF (for future problems)

the biggest thing they both share is the greatest common factor
in this case its

y

y