Greatest Common Factor of 36, 54 and 90 by Prime Factorization

Given Numbers: 36, 54, 90
Identify the Prime Factors of 36, 54 and 90 by Prime Factorization

• Prime Factorization of 36: 36 = 2 x 2 x 3 x 3 = 2² x 3²
• Prime Factorization of 54: 54 = 2 x 3 x 3 x 3 = 2¹ x 3³
• Prime Factorization of 90: 90 = 2 x 3 x 3 x 5 = 2¹ x 3² 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 36, 54 and 90

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

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

As a result, the Greatest Common Factor (GCF) of 36, 54 and 90 is equal to 2 x 3 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(36, 54, 90) = 2¹ x 3² = 2 x 3 x 3
• GCF(36, 54, 90) = 2 x 9
• GCF(36, 54, 90) = 18

Therefore, the Greatest Common Factor of 36, 54 and 90 by Prime Factorization = 18