Greatest Common Factor of 1,250 and 2,000 by Prime Factorization

Given Numbers: 1,250, 2,000
Identify the Prime Factors of 1,250 and 2,000 by Prime Factorization

• Prime Factorization of 1,250: 1,250 = 2 x 5 x 5 x 5 x 5 = 2¹ x 5⁴
• Prime Factorization of 2,000: 2,000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 = 2⁴ x 5³

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 1,250 and 2,000

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 at least 3 times in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 1,250 and 2,000 is equal to 2 x 5 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(1,250, 2,000) = 2¹ x 5³ = 2 x 5 x 5 x 5
• GCF(1,250, 2,000) = 2 x 125
• GCF(1,250, 2,000) = 250

Therefore, the Greatest Common Factor of 1,250 and 2,000 by Prime Factorization = 250