factor 18m - 24n using the gcf
To factor 18m - 24n using the greatest common factor (GCF), we need to find the largest common factor of 18 and 24 as well as the largest common factor of m and n.
First, let's find the GCF of 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 largest common factor of 18 and 24 is 6.
Next, let's find the GCF of m and n. Since we don't have any additional information about m and n, we assume they have no common factors other than 1.
Therefore, the GCF of m and n is 1.
Now, let's put it all together:
18m - 24n = (6 * 3m) - (6 * 4n)
= 6(3m - 4n)
So, the factored form 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 GCF of the coefficients (18 and 24) and the variables (m and n).
Step 1: Find the GCF of the coefficients:
The prime factorization of 18: 2 * 3 * 3
The prime factorization of 24: 2 * 2 * 2 * 3
The common prime factors are 2 * 3, so the GCF of 18 and 24 is 6.
Step 2: Find the GCF of the variables:
The variable m and n do not have any common factor, so the GCF of m and n is 1.
Step 3: Combine the GCF of the coefficients with the GCF of the variables:
The GCF of the coefficients is 6, and the GCF of the variables is 1. So, the GCF of 18m and 24n is 6.
Step 4: Divide each term by the GCF:
(18m) / 6 = 3m
(24n) / 6 = 4n
Step 5: Write the factored expression:
18m - 24n = (6)(3m) - (6)(4n)
= 6(3m - 4n)
Therefore, 18m - 24n can be factored as 6(3m - 4n).
To factor the expression 18m - 24n using the greatest common factor (GCF), we need to find the largest number or term that divides evenly into both 18m and 24n.
Step 1: Find the GCF of the coefficients
The coefficients of 18m and 24n are 18 and 24 respectively. To find the GCF of 18 and 24, you can list the factors of each and find the largest value they have in common.
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
The largest value they have in common is 6. So, the GCF of 18 and 24 is 6.
Step 2: Find the GCF of the variables
Now, let's look at the variables. The expression contains m and n, which means that they have no common factors other than 1.
Step 3: Combine the GCF of the coefficients and the variables
Since the GCF of the coefficients is 6, and there are no common factors between m and n, we can factor out 6 from both terms.
Factorization:
18m - 24n = 6(3m - 4n)
Thus, 18m - 24n can be factored as 6(3m - 4n).