Factor 18m − 24n

Question

using the GCF. (1 point)
Responses

​​​​​​​2(9m − 12n)
2 Left Parenthesis 9 m minus 12 n Right Parenthesis

​​​​​​​3(6m − 12n)
3 Left Parenthesis 6 m minus 12 n Right Parenthesis

​​​​​​​9(2m − 3n)
9 Left Parenthesis 2 m minus 3 n Right Parenthesis

​​​​​​​6(3m − 4n)

Answer 1

To factor the expression \( 18m - 24n \) using the greatest common factor (GCF), we start by finding the GCF of the coefficients 18 and 24.

The prime factorization of 18 is: \[ 18 = 2 \times 3^2 \]

The prime factorization of 24 is: \[ 24 = 2^3 \times 3 \]

The GCF is obtained by taking the lowest power of each common prime factor:

• For 2, the minimum power is \( 2^1 \).
• For 3, the minimum power is \( 3^1 \).

Thus, the GCF is: \[ 2^1 \times 3^1 = 6 \]

Now, we can factor \( 18m - 24n \) by dividing each term by the GCF, which is 6: \[ 18m - 24n = 6(3m - 4n) \]

Therefore, the correct factorization is: \[ 6(3m - 4n) \]

So the correct response is: 6(3m − 4n).