Greatest Common Factor of 24, 48 and 96 by Prime Factorization

Given Numbers: 24, 48, 96
Identify the Prime Factors of 24, 48 and 96 by Prime Factorization
  • Prime Factorization of 24: 24 = 2 x 2 x 2 x 3 = 23 x 31
  • Prime Factorization of 48: 48 = 2 x 2 x 2 x 2 x 3 = 24 x 31
  • Prime Factorization of 96: 96 = 2 x 2 x 2 x 2 x 2 x 3 = 25 x 31

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

  • 2 and 3 are Prime Factors common to the Prime Factorizations of 24, 48 and 96

Determine the least number of occurrences of 2 and 3 among the Prime Factorizations:

  • 2 occurs at least 3 times in each Prime Factorization
  • 3 occurs 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 24, 48 and 96 is equal to 2 x 2 x 2 x 3, which equals the product of 2 and 3 raised to the powers of their least number of occurrences or smallest exponent among the Prime Factorizations:

  • GCF(24, 48, 96) = 23 x 31 = 2 x 2 x 2 x 3
  • GCF(24, 48, 96) = 8 x 3
  • GCF(24, 48, 96) = 24

Therefore, the Greatest Common Factor of 24, 48 and 96 by Prime Factorization = 24

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