Greatest Common Factor of 80 and 200 by Prime Factorization

Given Numbers: 80, 200
Identify the Prime Factors of 80 and 200 by Prime Factorization

• Prime Factorization of 80: 80 = 2 x 2 x 2 x 2 x 5 = 2⁴ x 5¹
• Prime Factorization of 200: 200 = 2 x 2 x 2 x 5 x 5 = 2³ 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 80 and 200

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

• 2 occurs at least 3 times in each Prime Factorization
• 5 occurs at least 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 80 and 200 is equal to 2 x 2 x 2 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(80, 200) = 2³ x 5¹ = 2 x 2 x 2 x 5
• GCF(80, 200) = 8 x 5
• GCF(80, 200) = 40

Therefore, the Greatest Common Factor of 80 and 200 by Prime Factorization = 40