Greatest Common Factor of 33, 66 and 99 by Prime Factorization

Given Numbers: 33, 66, 99
Identify the Prime Factors of 33, 66 and 99 by Prime Factorization

• Prime Factorization of 33: 33 = 3 x 11 = 3¹ x 11¹
• Prime Factorization of 66: 66 = 2 x 3 x 11 = 2¹ x 3¹ x 11¹
• Prime Factorization of 99: 99 = 3 x 3 x 11 = 3² x 11¹

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

• 3 and 11 are Prime Factors common to the Prime Factorizations of 33, 66 and 99

Determine the least number of occurrences of 3 and 11 among the Prime Factorizations:

• 3 occurs at least 1 time in each Prime Factorization
• 11 occurs 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 33, 66 and 99 is equal to 3 x 11, which equals the product of 3 and 11 raised to the powers of their least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF(33, 66, 99) = 3¹ x 11¹
• GCF(33, 66, 99) = 3 x 11
• GCF(33, 66, 99) = 33

Therefore, the Greatest Common Factor of 33, 66 and 99 by Prime Factorization = 33