Greatest Common Factor of 26 and 91 by Prime Factorization

Given Numbers: 26, 91
Identify the Prime Factors of 26 and 91 by Prime Factorization

• Prime Factorization of 26: 26 = 2 x 13 = 2¹ x 13¹
• Prime Factorization of 91: 91 = 7 x 13 = 7¹ x 13¹

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

• 13 is the only Prime Factor common to the Prime Factorizations of 26 and 91

Determine the least number of occurrences of 13 among the Prime Factorizations:

• 13 occurs 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 26 and 91 is equal to 13, which equals 13 raised to the power of its least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF (26, 91) = 13¹
• GCF(26, 91) = 13

Therefore, the Greatest Common Factor of 26 and 91 by Prime Factorization = 13