Greatest Common Factor of 208 and 546 by Prime Factorization

Given Numbers: 208, 546
Identify the Prime Factors of 208 and 546 by Prime Factorization

• Prime Factorization of 208: 208 = 2 x 2 x 2 x 2 x 13 = 2⁴ x 13¹
• Prime Factorization of 546: 546 = 2 x 3 x 7 x 13 = 2¹ x 3¹ x 7¹ x 13¹

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

• 2 and 13 are Prime Factors common to the Prime Factorizations of 208 and 546

Determine the least number of occurrences of 2 and 13 among the Prime Factorizations:

• 2 occurs at least 1 time in each Prime Factorization
• 13 occurs 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 208 and 546 is equal to 2 x 13, which equals the product of 2 and 13 raised to the powers of their least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF(208, 546) = 2¹ x 13¹
• GCF(208, 546) = 2 x 13
• GCF(208, 546) = 26

Therefore, the Greatest Common Factor of 208 and 546 by Prime Factorization = 26