Greatest Common Factor of 9 and 27 by Prime Factorization

Given Numbers: 9, 27
Identify the Prime Factors of 9 and 27 by Prime Factorization

• Prime Factorization of 9: 9 = 3 x 3 = 3²
• Prime Factorization of 27: 27 = 3 x 3 x 3 = 3³

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 9 and 27

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

• 3 occurs at least 2 times in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 9 and 27 is equal to 3 x 3, which equals 3 raised to the power of its least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF(9, 27) = 3² = 3 x 3
• GCF(9, 27) = 9

Therefore, the Greatest Common Factor of 9 and 27 by Prime Factorization = 9