Greatest Common Factor of 12, 18, 30 and 32 by Prime Factorization

Given Numbers: 12, 18, 30, 32
Identify the Prime Factors of 12, 18, 30 and 32 by Prime Factorization

• Prime Factorization of 12: 12 = 2 x 2 x 3 = 2² x 3¹
• 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
• Prime Factorization of 32: 32 = 2 x 2 x 2 x 2 x 2 = 2⁵

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

• 2 is the only Prime Factor common to the Prime Factorizations of 12, 18, 30 and 32

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

• 2 occurs at least 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 12, 18, 30 and 32 is equal to 2, which equals 2 raised to the power of its least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF (12, 18, 30, 32) = 2¹
• GCF(12, 18, 30, 32) = 2

Therefore, the Greatest Common Factor of 12, 18, 30 and 32 by Prime Factorization = 2