Greatest Common Factor of 15 and 21 by Prime Factorization

Given Numbers: 15, 21
Identify the Prime Factors of 15 and 21 by Prime Factorization
  • Prime Factorization of 15: 15 = 3 x 5 = 31 x 51
  • Prime Factorization of 21: 21 = 3 x 7 = 31 x 71

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 15 and 21

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

  • 3 occurs 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 15 and 21 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 (15, 21) = 31
  • GCF(15, 21) = 3

Therefore, the Greatest Common Factor of 15 and 21 by Prime Factorization = 3

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