Question

Factor 18m − 24n using the GCF

Answer 1

[AI-generated answer — Bot GPT 3.5]

The greatest common factor (GCF) of 18m and 24n is 6.

To factor, we divide both terms by the GCF:

(18m/6) - (24n/6)

Simplifying, we get:

3m - 4n

Answer 2

Factor 18m − 24n using the GCF. (1 point)

Responses

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

​​​​​​​6(3m − 4n)
6 Left Parenthesis 3 m minus 4 n Right Parenthesis

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

​​​​​​​9(2m − 3n)

Answer 3

[AI-generated answer — Bot GPT 3.5]

The correct factorization of 18m - 24n using the GCF is:

6(3m - 4n)

Answer 4

[AI-generated answer — Explain Bot]

To factor the expression 18m - 24n using the Greatest Common Factor (GCF), we need to find the largest common factor of the terms 18m and 24n.

Step 1: Find the GCF of 18m and 24n.
To find the GCF, we break down each term into its prime factors.

The prime factors of 18m are:
18 = 2 * 3 * 3
m = m (m is already a prime factor)

The prime factors of 24n are:
24 = 2 * 2 * 2 * 3
n = n (n is already a prime factor)

Step 2: Identify the common factors.
The only common factor between 18m and 24n is 2.

Step 3: Determine the exponent of the GCF.
The exponent of the GCF is the minimum power of 2 that appears in both terms. In this case, the exponent of 2 in 18m is 1, and the exponent of 2 in 24n is also 1. Therefore, the exponent of the GCF is 1.

Step 4: Write the factored expression.
Now, we can factor out the GCF from the original expression and write it as the product of the GCF and the remaining terms:

GCF * (quotient of 18m/GCF - quotient of 24n/GCF)

Factoring out the GCF of 2, we get:

2 * (9m - 12n)

Therefore, the factored form of 18m - 24n using the GCF is 2(9m - 12n).