Greatest Common Factor of 375 and 1,000 by Prime Factorization

Given Numbers: 375, 1,000
Identify the Prime Factors of 375 and 1,000 by Prime Factorization

• Prime Factorization of 375: 375 = 3 x 5 x 5 x 5 = 3¹ x 5³
• Prime Factorization of 1,000: 1,000 = 2 x 2 x 2 x 5 x 5 x 5 = 2³ x 5³

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 375 and 1,000

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

• 5 occurs 3 times in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 375 and 1,000 is equal to 5 x 5 x 5, which equals 5 raised to the power of its least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF(375, 1,000) = 5³ = 5 x 5 x 5
• GCF(375, 1,000) = 125

Therefore, the Greatest Common Factor of 375 and 1,000 by Prime Factorization = 125