Greatest Common Factor of 64 and 240 by Prime Factorization

Given Numbers: 64, 240
Identify the Prime Factors of 64 and 240 by Prime Factorization

• Prime Factorization of 64: 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2⁶
• Prime Factorization of 240: 240 = 2 x 2 x 2 x 2 x 3 x 5 = 2⁴ x 3¹ x 5¹

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

• 2 is the only Prime Factor common to the Prime Factorizations of 64 and 240

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

• 2 occurs at least 4 times in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 64 and 240 is equal to 2 x 2 x 2 x 2, which equals 2 raised to the power of its least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF(64, 240) = 2⁴ = 2 x 2 x 2 x 2
• GCF(64, 240) = 16

Therefore, the Greatest Common Factor of 64 and 240 by Prime Factorization = 16