Greatest Common Factor of 18 and 30 by Prime Factorization

Given Numbers: 18, 30
Identify the Prime Factors of 18 and 30 by Prime Factorization

• Prime Factorization of 18: 18 = 2 x 3 x 3 = 2¹ x 3²
• Prime Factorization of 30: 30 = 2 x 3 x 5 = 2¹ x 3¹ x 5¹

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

• 2 and 3 are Prime Factors common to the Prime Factorizations of 18 and 30

Determine the least number of occurrences of 2 and 3 among the Prime Factorizations:

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

As a result, the Greatest Common Factor (GCF) of 18 and 30 is equal to 2 x 3, which equals the product of 2 and 3 raised to the powers of their least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF(18, 30) = 2¹ x 3¹
• GCF(18, 30) = 2 x 3
• GCF(18, 30) = 6

Therefore, the Greatest Common Factor of 18 and 30 by Prime Factorization = 6