Factor 18m − 24n using the GCF. (1 point)%0D%0AResponses%0D%0A%0D%0A%E2%80%8B%E2%80%8B%E2%80%8B%E2%80%8B%E2%80%8B%E2%80%8B%E2%80%8B9(2m − 3n)%0D%0A9 Left Parenthesis 2 m minus 3 n Right Parenthesis%0D%0A%0D%0A%E2%80%8B%E2%80%8B%E2%80%8B%E2%80%8B%E2%80%8B%E2%80%8B%E2%80%8B6(3m − 4n)%0D%0A6 Left Parenthesis 3 m minus 4 n Right Parenthesis%0D%0A%0D%0A%E2%80%8B%E2%80%8B%E2%80%8B%E2%80%8B%E2%80%8B%E2%80%8B%E2%80%8B2(9m − 12n)%0D%0A2 Left Parenthesis 9 m minus 12 n Right Parenthesis%0D%0A%0D%0A%E2%80%8B%E2%80%8B%E2%80%8B%E2%80%8B%E2%80%8B%E2%80%8B%E2%80%8B3(6m − 12n)
The correct factorization of 18m - 24n using the GCF is 6(3m - 4n).
To factor 18m - 24n using the greatest common factor (GCF), we need to find the largest common factor of both 18m and 24n.
Step 1: Find the GCF of 18m and 24n.
The prime factorization of 18m is 2 * 3^2 * m.
The prime factorization of 24n is 2^3 * 3 * n.
The common factors between 18m and 24n are 2 and 3.
Step 2: Factor out the GCF.
Since the GCF is 2 * 3 = 6, we can factor it out:
18m - 24n = 6(3m - 4n)
Therefore, the factored form of 18m - 24n using the GCF is 6(3m - 4n).
To factor 18m − 24n using the GCF (Greatest Common Factor), we need to find the largest common factor of the coefficients 18 and 24, as well as the variables m and n.
Step 1: Find the GCF of the coefficients 18 and 24.
The factors of 18 are: 1, 2, 3, 6, 9, and 18.
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24.
The common factors are: 1, 2, 3, and 6.
The largest common factor is 6.
Step 2: Divide each term by the GCF.
Divide 18m by 6: 18m ÷ 6 = 3m.
Divide -24n by 6: -24n ÷ 6 = -4n.
Step 3: Write the expression using the factored terms.
The factored expression is: 6(3m − 4n).
Therefore, the expression 18m − 24n can be factored as 6(3m − 4n).