Greatest Common Factor of 25 and 65 by Prime Factorization

Given Numbers: 25, 65
Identify the Prime Factors of 25 and 65 by Prime Factorization
  • Prime Factorization of 25: 25 = 5 x 5 = 52
  • Prime Factorization of 65: 65 = 5 x 13 = 51 x 131

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

  • 5 is the only Prime Factor common to the Prime Factorizations of 25 and 65

Determine the least number of occurrences of 5 among the Prime Factorizations:

  • 5 occurs at least 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 25 and 65 is equal to 5, which equals 5 raised to the power of its least number of occurrences or smallest exponent among the Prime Factorizations:

  • GCF (25, 65) = 51
  • GCF(25, 65) = 5

Therefore, the Greatest Common Factor of 25 and 65 by Prime Factorization = 5

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