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Which of the following expresses 12 + 42 by using the GCF of the two numbers? 3(9 + 14) 3(4 + 38) 6(2 + 7) 6(6 + 36)

Verified Answer :

konrad509

\(GCF(12,42)=6\\\\ 12 + 42=6(2+7)\)

The expression that expresses 12 + 42 by using the GCF is 6(2 + 7). The correct option is the third option 6(2 + 7)

To determine which of the given options expresses the given expression (12 + 42) by using the GCF (Greatest common factor),

First, we will list the factors of the numbers in the given expression

The numbers are 12 and 42

  • The factors of 12 are

1, 2, 3, 4, 6 and 12

  • The factors of 42 are

1, 2, 3, 6, 7, 14, 21 and 42

From above, we can observe that the greatest common factor of 12 and 42 is 6.

Now, we will factorize the given expression, using the greatest common factor (GCF)

The expression is 12 + 42

Factorizing

12 + 42 = 6(2 + 7)

Hence, the expression that expresses 12 + 42 by using the GCF is 6(2 + 7). The correct option is the third option 6(2 + 7)

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