Greatest Common Factor of 12, 15 and 21 by Prime Factorization

Given Numbers: 12, 15, 21
Identify the Prime Factors of 12, 15 and 21 by Prime Factorization

• Prime Factorization of 12: 12 = 2 x 2 x 3 = 2² x 3¹
• Prime Factorization of 15: 15 = 3 x 5 = 3¹ x 5¹
• Prime Factorization of 21: 21 = 3 x 7 = 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 12, 15 and 21

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

• 3 occurs 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 12, 15 and 21 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 (12, 15, 21) = 3¹
• GCF(12, 15, 21) = 3

Therefore, the Greatest Common Factor of 12, 15 and 21 by Prime Factorization = 3