Greatest Common Factor of 50 and 100 by Prime Factorization

Given Numbers: 50, 100
Identify the Prime Factors of 50 and 100 by Prime Factorization

• Prime Factorization of 50: 50 = 2 x 5 x 5 = 2¹ x 5²
• Prime Factorization of 100: 100 = 2 x 2 x 5 x 5 = 2² x 5²

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

• 2 and 5 are Prime Factors common to the Prime Factorizations of 50 and 100

Determine the least number of occurrences of 2 and 5 among the Prime Factorizations:

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

As a result, the Greatest Common Factor (GCF) of 50 and 100 is equal to 2 x 5 x 5, which equals the product of 2 and 5 raised to the powers of their least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF(50, 100) = 2¹ x 5² = 2 x 5 x 5
• GCF(50, 100) = 2 x 25
• GCF(50, 100) = 50

Therefore, the Greatest Common Factor of 50 and 100 by Prime Factorization = 50