Factor 48y+36z using the GCF
To factor 48y + 36z using the greatest common factor (GCF), we need to find the greatest common factor of 48 and 36.
The prime factorization of 48 is 2^4 * 3, and the prime factorization of 36 is 2^2 * 3^2.
The GCF of 48 and 36 is 2^2 * 3 = 12.
Therefore, we can factor out 12 from 48y and 36z:
48y + 36z = 12(4y + 3z)
To factor out the greatest common factor (GCF) of 48y and 36z, we need to find the common factors of these two terms.
The prime factorization of 48 can be found by dividing it by prime numbers:
48 = 2 × 2 × 2 × 2 × 3 = 2^4 × 3
Similarly, the prime factorization of 36 is:
36 = 2 × 2 × 3 × 3 = 2^2 × 3^2
Now let's look at the variables. The GCF of y and z is simply 1 since they have no common factors other than 1.
Therefore, the GCF of 48y and 36z is 2^2 × 3 = 12.
To factor out the GCF from 48y and 36z, we divide each term by 12:
48y ÷ 12 = 4y
36z ÷ 12 = 3z
So the factored form of 48y + 36z using the GCF is 12(4y + 3z).
To factor the expression 48y + 36z using the greatest common factor (GCF), we need to identify the common factors of the coefficients 48 and 36, as well as the variables y and z.
Step 1: Find the GCF of the coefficients 48 and 36. The GCF of 48 and 36 is 12. Both numbers are divisible by 12 without any remainder.
Step 2: Determine the GCF of the variables y and z. Since there are no common factors between y and z, the GCF of y and z is 1.
Step 3: Combine the GCF of the coefficients and the GCF of the variables to factor the expression. The factored form becomes:
12(4y + 3z)
Therefore, 48y + 36z can be factored as 12(4y + 3z), using the GCF.