Greatest Common Factor of 68 and 88 by Prime Factorization

Given Numbers: 68, 88
Identify the Prime Factors of 68 and 88 by Prime Factorization

• Prime Factorization of 68: 68 = 2 x 2 x 17 = 2² x 17¹
• Prime Factorization of 88: 88 = 2 x 2 x 2 x 11 = 2³ x 11¹

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 68 and 88

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 68 and 88 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(68, 88) = 2² = 2 x 2
• GCF(68, 88) = 4

Therefore, the Greatest Common Factor of 68 and 88 by Prime Factorization = 4