Find the GCF of 32 and 48

Answer 1

To find the greatest common factor (GCF) of 32 and 48, we can use the prime factorization method.

First, we find the prime factors of each number:

• 32:

  • 32 = 2 × 16
  • 16 = 2 × 8
  • 8 = 2 × 4
  • 4 = 2 × 2
  • So, the prime factorization of 32 is \( 2^5 \).

• 48:

  • 48 = 2 × 24
  • 24 = 2 × 12
  • 12 = 2 × 6
  • 6 = 2 × 3
  • So, the prime factorization of 48 is \( 2^4 × 3^1 \).

Now, we find the common prime factors and their lowest powers:

• The prime factor common to both 32 and 48 is \( 2 \).
• The lowest power of \( 2 \) in the prime factorization of both numbers is \( 2^4 \).

Thus, the GCF of 32 and 48 is \( 2^4 = 16 \).

Therefore, the GCF of 32 and 48 is 16.