Factor $48m+42n$ to identify the equivalent expressions. $\newline$ Choose $2$ answers: $\newline$ A $6(8m+7n)$ $\newline$ B $3(16m+14n)$ $\newline$ C $2(12m+21n)$ $\newline$ D $7(7m+6n)$

Full solution

Q. Factor

48m+42n

to identify the equivalent expressions.

\newline

Choose

2

answers:

\newline

6(8m+7n)

\newline

3(16m+14n)

\newline

2(12m+21n)

\newline

7(7m+6n)

Identify GCF of Coefficients: Identify the greatest common factor (GCF) of the coefficients $48$ and $42$ . The factors of $48$ are $1, 2, 3, 4, 6, 8, 12, 16, 24, 48$ . The factors of $42$ are $1, 2, 3, 6, 7, 14, 21, 42$ . The GCF of $48$ and $42$ is $6$ .
Divide by GCF: Divide both terms of the expression $48m + 42n$ by the GCF, which is $6$ . $\newline$ $48m \div 6 = 8m$ $\newline$ $42n \div 6 = 7n$ $\newline$ So, $48m + 42n$ factored by $6$ is $6(8m + 7n)$ .
Check Other Options: Check if any of the other answer choices are equivalent to $6(8m + 7n)$ .
Option B: $3(16m + 14n)$ is not equivalent because $16m + 14n$ is not the result of dividing $48m + 42n$ by $3$ .
Option C: $2(12m + 21n)$ is not equivalent because $12m + 21n$ is not the result of dividing $48m + 42n$ by $2$ .
Option D: $7(7m + 6n)$ is not equivalent because $3(16m + 14n)$ $0$ is not the result of dividing $48m + 42n$ by $3(16m + 14n)$ $2$ .