Factor 24n−32 using the GCF
To factor out the greatest common factor (GCF) of 24n and -32, we first need to find the GCF of these two terms.
The prime factorization of 24n is 2^3 * 3 * n.
The prime factorization of -32 is -1 * 2^5.
To find the GCF, we take the lowest power of each common prime factor. In this case, the common prime factor is 2 and the lowest power is 2^3.
So, the GCF of 24n and -32 is 2^3 = 8.
Now, we can factor out the GCF from 24n and -32:
24n - 32 = 8(3n - 4).
Therefore, 24n - 32 can be factored as 8(3n - 4) using the GCF.
what is the answer
The factored form of 24n - 32 using the greatest common factor (GCF) is 8(3n - 4).
To factor 24n-32 using the greatest common factor (GCF), we need to find the common factor of both terms.
Step 1: Find the GCF of 24 and 32.
The prime factorization of 24 is 2 * 2 * 2 * 3.
The prime factorization of 32 is 2 * 2 * 2 * 2 * 2.
The common factors are 2 * 2 * 2 = 8.
Step 2: Factor out the GCF from both terms.
To factor out the GCF of 8, divide each term by 8.
The expression becomes:
8(3n - 4)
So, 24n-32 can be factored as 8(3n-4).
To factor the given expression 24n - 32 using the Greatest Common Factor (GCF), we first need to find the GCF of the two terms. In this case, the GCF of 24n and 32 is 8.
Step 1: Find the GCF
- The prime factorization of 24n can be written as 2 x 2 x 2 x 3 x n.
- The prime factorization of 32 can be written as 2 x 2 x 2 x 2 x 2.
- The common factors between the two terms are 2 x 2 x 2, which equals 8.
Step 2: Divide both terms by the GCF
By dividing 24n by 8, we get (24n / 8) = 3n.
By dividing 32 by 8, we get (32 / 8) = 4.
Step 3: Rewrite the expression
Now we can express the original expression, 24n - 32, as follows:
24n - 32 = 8 x 3n - 8 x 4.
Step 4: Factor out the GCF
We can now factor out the GCF from the expression:
24n - 32 = 8(3n - 4).
Therefore, the expression 24n - 32 can be factored as 8(3n - 4), using the GCF of 8.