Find the GCF of 18 and 27

Answer 1

To find the greatest common factor (GCF) of 18 and 27, we can use the prime factorization method:

1. Prime factorization of 18:

   • 18 = 2 × 3 × 3 = 2 × 3²

2. Prime factorization of 27:

   • 27 = 3 × 3 × 3 = 3³

3. Identify the common prime factors:

   • The common prime factor between 18 and 27 is 3.

4. Determine the lowest power of the common prime factors:

   • For the factor of 3: The minimum of the powers in both factorizations is 2 (from 3² in 18).

5. Calculate the GCF:

   • GCF = 3² = 9

Therefore, the greatest common factor of 18 and 27 is 9.