Greatest Common Factor of 24 and 100 by Prime Factorization

Given Numbers: 24, 100
Identify the Prime Factors of 24 and 100 by Prime Factorization
  • Prime Factorization of 24: 24 = 2 x 2 x 2 x 3 = 23 x 31
  • Prime Factorization of 100: 100 = 2 x 2 x 5 x 5 = 22 x 52

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

  • 2 is the only Prime Factor common to the Prime Factorizations of 24 and 100

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

  • 2 occurs at least 2 times in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 24 and 100 is equal to 2 x 2, which equals 2 raised to the power of its least number of occurrences or smallest exponent among the Prime Factorizations:

  • GCF(24, 100) = 22 = 2 x 2
  • GCF(24, 100) = 4

Therefore, the Greatest Common Factor of 24 and 100 by Prime Factorization = 4

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