Given the sum 100 equals 64 + 36 rewrite 64 + 36 using third GCF and multiplication A 2(32 + 18 ) B 4 (16 + 9) C 1 (64 + 36) D 4 (16x9)

1 answer

To rewrite \(64 + 36\) using the greatest common factor (GCF) and multiplication, we first need to find the GCF of \(64\) and \(36\).

  1. Prime factorization:

    • \(64 = 2^6\)
    • \(36 = 2^2 \times 3^2\)
  2. Finding the GCF:

    • The common factor is \(2\), and the smallest power is \(2^2\).
    • Thus, GCF = \(4\).
  3. 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: \(4(16 + 9)\).