Greatest Common Factor of 36 and 44 by Prime Factorization

Given Numbers: 36, 44
Identify the Prime Factors of 36 and 44 by Prime Factorization

• Prime Factorization of 36: 36 = 2 x 2 x 3 x 3 = 2² x 3²
• Prime Factorization of 44: 44 = 2 x 2 x 11 = 2² x 11¹

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 36 and 44

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

• 2 occurs 2 times in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 36 and 44 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(36, 44) = 2² = 2 x 2
• GCF(36, 44) = 4

Therefore, the Greatest Common Factor of 36 and 44 by Prime Factorization = 4