Well, honey, the greatest common factor in 21ab and 14b is 7b. You see, 21 can be broken down into 3 x 7, and 14 can be broken down into 2 x 7. And since they both have a b in common, that's your greatest common factor right there. Math made sassy!
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Oh, dude, the greatest common factor in 21ab and 14b is 7b. You just gotta look at the numbers and variables and find the biggest one that they both share. It's like finding the coolest party that both 21ab and 14b want to go to.