We can see that b is a common factor. This leaves us with 8 and 12 for which the gcf is 4. So the gcf of 8b and 12b is 4b.

Note, if there are two different powers of the same variable in the two expressions, then the smaller power of b would appear in the answer (e.g. the gcf of 8b^{5} and 12b^{3} would be 4b^{3}). If a variable appears in only one expression, it will not appear in the gcf.

For 36r^{2} and 18rq:

Note that the gcf of 36 and 18 is 18. Thus the gcd of 36r^{2} and 18rq is 18r.

i sincerely appreciate your help this is very detailed and to the point. i understand it now and appreciate the help with expaining how to determine the correct answer without all the mumbo jumbo that comes with getting the answers.

Patricia G. | Family ESL or Spanish Teacher; Corporate ESL/English CoachFamily ESL or Spanish Teacher; Corporate...

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Thank you, Roman, for providing students with the full details; it always helps them to explain it further. We, as educators, sometimes forget that our students--as well as teachers in other disciplines--don't have the same background of knowledge that we have, in their heads.

Tamara J. | Math Tutoring - Algebra and Calculus (all levels)Math Tutoring - Algebra and Calculus (al...

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The Greatest Common Factor, or GCF, is the highest number/expression that divides into a set of numbers/expressions evenly without a remainder.

For 8b and 12b, first notice that both expressions have a common variable (that being 'b') that can be factored out of both expressions. Then, if we list the common divisors of both 8 and 12, we can find the greatest common divisor between both numbers:

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