Greatest Common Factor of 15 and 45 by Prime Factorization

Given Numbers: 15, 45
Identify the Prime Factors of 15 and 45 by Prime Factorization

• Prime Factorization of 15: 15 = 3 x 5 = 3¹ x 5¹
• Prime Factorization of 45: 45 = 3 x 3 x 5 = 3² x 5¹

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

• 3 and 5 are Prime Factors common to the Prime Factorizations of 15 and 45

Determine the least number of occurrences of 3 and 5 among the Prime Factorizations:

• 3 occurs at least 1 time in each Prime Factorization
• 5 occurs 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 15 and 45 is equal to 3 x 5, which equals the product of 3 and 5 raised to the powers of their least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF(15, 45) = 3¹ x 5¹
• GCF(15, 45) = 3 x 5
• GCF(15, 45) = 15

Therefore, the Greatest Common Factor of 15 and 45 by Prime Factorization = 15