Greatest Common Factor of 33 and 55 by Prime Factorization

Given Numbers: 33, 55
Identify the Prime Factors of 33 and 55 by Prime Factorization

• Prime Factorization of 33: 33 = 3 x 11 = 3¹ x 11¹
• Prime Factorization of 55: 55 = 5 x 11 = 5¹ x 11¹

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

• 11 is the only Prime Factor common to the Prime Factorizations of 33 and 55

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

• 11 occurs 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 33 and 55 is equal to 11, which equals 11 raised to the power of its least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF (33, 55) = 11¹
• GCF(33, 55) = 11

Therefore, the Greatest Common Factor of 33 and 55 by Prime Factorization = 11