Factor 48y+36z using GCF
A. 6(8y+6x)
B. 12(4y+3z)
C. 4(12y+9z)
D. 16(3y+2x)
A. 6(8y+6x)
B. 12(4y+3z)
C. 4(12y+9z)
D. 16(3y+2x)
Answers
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Answered by
GPT-4o mini
To factor the expression \( 48y + 36z \) using its greatest common factor (GCF):
1. **Identify the coefficients:** The coefficients are 48 and 36.
2. **Find the GCF of these coefficients:**
- The prime factorization of 48 is \( 2^4 \times 3 \).
- The prime factorization of 36 is \( 2^2 \times 3^2 \).
- The GCF is found by taking the lowest power of each common prime factor:
- For 2, the minimum power is \( 2^2 = 4 \).
- For 3, the minimum power is \( 3^1 = 3 \).
- Therefore, the GCF of 48 and 36 is \( 4 \times 3 = 12 \).
3. **Factor out the GCF from the expression:**
\[
48y + 36z = 12(4y + 3z)
\]
Thus, the expression can be factored as \( 12(4y + 3z) \).
The correct answer is **B. 12(4y + 3z)**.
1. **Identify the coefficients:** The coefficients are 48 and 36.
2. **Find the GCF of these coefficients:**
- The prime factorization of 48 is \( 2^4 \times 3 \).
- The prime factorization of 36 is \( 2^2 \times 3^2 \).
- The GCF is found by taking the lowest power of each common prime factor:
- For 2, the minimum power is \( 2^2 = 4 \).
- For 3, the minimum power is \( 3^1 = 3 \).
- Therefore, the GCF of 48 and 36 is \( 4 \times 3 = 12 \).
3. **Factor out the GCF from the expression:**
\[
48y + 36z = 12(4y + 3z)
\]
Thus, the expression can be factored as \( 12(4y + 3z) \).
The correct answer is **B. 12(4y + 3z)**.
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