Greatest Common Factor of 36, 60 and 84 by Prime Factorization

Given Numbers: 36, 60, 84
Identify the Prime Factors of 36, 60 and 84 by Prime Factorization

• Prime Factorization of 36: 36 = 2 x 2 x 3 x 3 = 2² x 3²
• Prime Factorization of 60: 60 = 2 x 2 x 3 x 5 = 2² x 3¹ x 5¹
• Prime Factorization of 84: 84 = 2 x 2 x 3 x 7 = 2² x 3¹ x 7¹

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, 60 and 84

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

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

As a result, the Greatest Common Factor (GCF) of 36, 60 and 84 is equal to 2 x 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(36, 60, 84) = 2² x 3¹ = 2 x 2 x 3
• GCF(36, 60, 84) = 4 x 3
• GCF(36, 60, 84) = 12

Therefore, the Greatest Common Factor of 36, 60 and 84 by Prime Factorization = 12