Greatest Common Factor of 50, 75 and 100 by Prime Factorization

Given Numbers: 50, 75, 100
Identify the Prime Factors of 50, 75 and 100 by Prime Factorization

• Prime Factorization of 50: 50 = 2 x 5 x 5 = 2¹ x 5²
• Prime Factorization of 75: 75 = 3 x 5 x 5 = 3¹ 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:

• 5 is the only Prime Factor common to the Prime Factorizations of 50, 75 and 100

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

• 5 occurs 2 times in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 50, 75 and 100 is equal to 5 x 5, which equals 5 raised to the power of its least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF(50, 75, 100) = 5² = 5 x 5
• GCF(50, 75, 100) = 25

Therefore, the Greatest Common Factor of 50, 75 and 100 by Prime Factorization = 25