Greatest Common Factor of 27 and 42 by Prime Factorization

Given Numbers: 27, 42
Identify the Prime Factors of 27 and 42 by Prime Factorization

• Prime Factorization of 27: 27 = 3 x 3 x 3 = 3³
• Prime Factorization of 42: 42 = 2 x 3 x 7 = 2¹ x 3¹ x 7¹

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

• 3 is the only Prime Factor common to the Prime Factorizations of 27 and 42

Determine the least number of occurrences of 3 among the Prime Factorizations:

• 3 occurs at least 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 27 and 42 is equal to 3, which equals 3 raised to the power of its least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF (27, 42) = 3¹
• GCF(27, 42) = 3

Therefore, the Greatest Common Factor of 27 and 42 by Prime Factorization = 3