Greatest Common Factor of 6, 9 and 15 by Prime Factorization

Given Numbers: 6, 9, 15
Identify the Prime Factors of 6, 9 and 15 by Prime Factorization
  • Prime Factorization of 6: 6 = 2 x 3 = 21 x 31
  • Prime Factorization of 9: 9 = 3 x 3 = 32
  • Prime Factorization of 15: 15 = 3 x 5 = 31 x 51

Determine the Prime Factor(s) that are common to the Prime Factorization of each number:

  • 3 is the only Prime Factor common to the Prime Factorizations of 6, 9 and 15

Determine the least number of occurrences of 3 among the Prime Factorizations:

  • 3 occurs at least 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 6, 9 and 15 is equal to 3, which equals 3 raised to the power of its least number of occurrences or smallest exponent among the Prime Factorizations:

  • GCF (6, 9, 15) = 31
  • GCF(6, 9, 15) = 3

Therefore, the Greatest Common Factor of 6, 9 and 15 by Prime Factorization = 3

The solution above and other related solutions were provided by the GCF by Prime Factorization Application.