Question

Which uses the GCF to generate an expression equivalent to 24v-84?

O3(8V-28)
O 6(4v-14)
O 12(2v-7)
O 24(V-60)

Answer 1

(c) 12(2v-7)

Explanation:

You want the expression resulting from factoring out the greatest common factor from the sum 24v -84.

GCF

The greatest common factor here is the GCF of 24 and 84. We note that ...

24 = 12·2

84 = 12·7

and 2 and 7 have no common factors. Then the GCF of 24 and 84 is 12.

The factored expression is ...

24v -84 = 12(2v -7)

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Additional comment

The GCF can also be found by considering the remainder from dividing 84 by 24. That remainder is 12, which divides both numbers with a remainder of 0. Hence 12 is the GCF.

If the remainder did not divide both numbers with a remainder of 0, then the process is repeated to find the GCF of the smaller number (24) and the remainder. (This is a description of Euclid's algorithm for finding the GCF.)