Greatest Common Factor of 24, 32 and 40 by Prime Factorization

Given Numbers: 24, 32, 40
Identify the Prime Factors of 24, 32 and 40 by Prime Factorization

• Prime Factorization of 24: 24 = 2 x 2 x 2 x 3 = 2³ x 3¹
• Prime Factorization of 32: 32 = 2 x 2 x 2 x 2 x 2 = 2⁵
• Prime Factorization of 40: 40 = 2 x 2 x 2 x 5 = 2³ 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 24, 32 and 40

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

• 2 occurs at least 3 times in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 24, 32 and 40 is equal to 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(24, 32, 40) = 2³ = 2 x 2 x 2
• GCF(24, 32, 40) = 8

Therefore, the Greatest Common Factor of 24, 32 and 40 by Prime Factorization = 8