To rewrite \(64 + 36\) using the greatest common factor (GCF) and multiplication, we first need to find the GCF of \(64\) and \(36\).
-
Prime factorization:
- \(64 = 2^6\)
- \(36 = 2^2 \times 3^2\)
-
Finding the GCF:
- The common factor is \(2\), and the smallest power is \(2^2\).
- Thus, GCF = \(4\).
-
Expressing \(64 + 36\) using the GCF:
- Factoring out \(4\): \[ 64 + 36 = 4(16 + 9) \]
Therefore, the rewritten form of \(64 + 36\) using the GCF of \(4\) is \(4(16 + 9)\).
Among the options given:
- A) \(2(32 + 18)\)
- B) \(4(16 + 9)\)
- C) \(1(64 + 36)\)
- D) \(4(16 \times 9)\)
The correct answer is B: \(4(16 + 9)\).