Factor 48y + 36z using the GCF
To factor 48y + 36z using the greatest common factor (GCF), we need to determine the GCF of 48 and 36.
The prime factorization of 48 is 2^4 * 3, and the prime factorization of 36 is 2^2 * 3^2.
To find the GCF, we take the smallest exponent of each common prime factor, which is 2^2 * 3 = 12.
Now, we can rewrite 48y + 36z as the product of the GCF and the quotient when dividing each term by the GCF:
12(4y + 3z)
To factor out the greatest common factor (GCF) of 48y and 36z, we need to find the largest number that divides evenly into both terms. Let's start by finding the prime factors of each term:
48y = 2 * 2 * 2 * 2 * 3 * y
36z = 2 * 2 * 3 * 3 * z
Next, we identify the common factors:
The common factors are 2 * 2 * 3, which is equal to 12.
Now, let's factor out the GCF from both terms:
48y + 36z = 12(4y + 3z)
Therefore, the expression 48y + 36z can be factored as 12(4y + 3z) using the GCF.
To factor 48y + 36z using the GCF (Greatest Common Factor), we need to find the largest number that divides both 48y and 36z.
Step 1: Find the GCF of the coefficients (48 and 36).
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The largest number that divides both 48 and 36 is 12.
Step 2: Find the GCF of the variables (y and z).
Since y and z have different variables, the GCF of their coefficients would be 1.
Now, we can write the expression as the product of the GCF and the quotient.
48y + 36z = 12(4y + 3z)
Therefore, the factored form of 48y + 36z using the GCF is 12(4y + 3z).