factor 48 + 36z using the gcf
To factor the expression 48 + 36z using the greatest common factor (GCF), we need to find the common factors of 48 and 36z.
First, find the prime factorization of 48:
48 = 2 * 2 * 2 * 2 * 3
Next, find the GCF of 48 and 36z by looking at the common factors:
The common factors of 48 and 36z are 2 and 3.
Now, factor out the GCF from the expression:
48 + 36z = 2 * 2 * 2 * 2 * 3 + 2 * 2 * 3 * z
= 2 * 2 * 3 * (2 + z)
So, the final factored form using the GCF is 2 * 2 * 3 * (2 + z).
To factor the expression 48 + 36z using the greatest common factor (GCF), we need to find the largest number that divides evenly into both 48 and 36z. The GCF of 48 and 36z is 12, so we can factor out 12 from both terms.
First, let's factor out 12 from 48:
48 divided by 12 equals 4, so we can rewrite 48 as 12 * 4.
Next, let's factor out 12 from 36z:
36z divided by 12 equals 3z, so we can rewrite 36z as 12 * 3z.
Now, let's rewrite the original expression using the factored terms:
48 + 36z = 12 * 4 + 12 * 3z
Now, we can factor out the common factor of 12:
48 + 36z = 12(4 + 3z)
So, the expression 48 + 36z factored with the GCF is 12(4 + 3z).
To factor a given expression using the greatest common factor (GCF), you need to find the GCF of all the terms and then divide each term by the GCF. Let's break it down step by step.
Step 1: Identify the terms in the expression.
The given expression is 48 + 36z. It has two terms: 48 and 36z.
Step 2: Find the GCF of the terms.
To find the GCF, you need to determine the greatest common factor that divides evenly into both terms. Let's find the GCF of 48 and 36.
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
The common factors of 48 and 36 are 1, 2, 3, 4, 6, and 12. The greatest common factor is 12.
Step 3: Divide each term by the GCF.
To factor the expression, divide each term by the GCF (12).
48/12 = 4
36z/12 = 3z
The factored form of 48 + 36z using the GCF is 4 + 3z.