Greatest Common Factor of 12 and 32 by Prime Factorization

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

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

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

• 2 occurs at least 2 times in each Prime Factorization

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

• GCF(12, 32) = 2² = 2 x 2
• GCF(12, 32) = 4

Therefore, the Greatest Common Factor of 12 and 32 by Prime Factorization = 4