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. The GCF of 18 and 24 is 6.
We can then factor out the GCF from each term:
18m = 6 * 3 * m = 6m
24n = 6 * 4 * n = 6n
So, 18m - 24n can be factored as 6(3m - 4n).
To factor the expression 18m - 24n using the greatest common factor (GCF), you first need to find the GCF of the two terms.
Step 1: Find the GCF
The GCF is the largest common factor that divides both 18m and 24n evenly. Let's break down each term into its prime factors.
18m = 2 * 3 * 3 * m
24n = 2 * 2 * 2 * 3 * n
From these prime factorizations, we can see that the common factors are 2 and 3. The GCF is the product of these common factors: GCF = 2 * 3 = 6.
Step 2: Divide each term by the GCF
Now that we have the GCF, we can factor out the GCF from each term by dividing it.
18m / 6 = 3m
24n / 6 = 4n
Step 3: Write the factored expression
We divide each term by the GCF to get the factored expression:
18m - 24n = 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 largest common factor of both 18m and 24n.
Step 1: Find the GCF of the coefficients 18 and 24.
The prime factors of 18 are 2 * 3 * 3.
The prime factors of 24 are 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 variables in 18m are m, and in 24n, the variable is n.
Since there are no common variables, the GCF of the variables is 1.
Step 3: Multiply 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 the original expression by the GCF.
(18m-24n) / 6 = 3m-4n.
So, the factored form of 18m-24n using the GCF is 6(3m-4n).