Greatest Common Factor of 34 and 51 by Prime Factorization

Given Numbers: 34, 51
Identify the Prime Factors of 34 and 51 by Prime Factorization

• Prime Factorization of 34: 34 = 2 x 17 = 2¹ x 17¹
• Prime Factorization of 51: 51 = 3 x 17 = 3¹ x 17¹

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

• 17 is the only Prime Factor common to the Prime Factorizations of 34 and 51

Determine the least number of occurrences of 17 among the Prime Factorizations:

• 17 occurs 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 34 and 51 is equal to 17, which equals 17 raised to the power of its least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF (34, 51) = 17¹
• GCF(34, 51) = 17

Therefore, the Greatest Common Factor of 34 and 51 by Prime Factorization = 17