Greatest Common Factor of 48 and 72 by Prime Factorization

Given Numbers: 48, 72
Identify the Prime Factors of 48 and 72 by Prime Factorization

• Prime Factorization of 48: 48 = 2 x 2 x 2 x 2 x 3 = 2⁴ x 3¹
• Prime Factorization of 72: 72 = 2 x 2 x 2 x 3 x 3 = 2³ x 3²

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

• 2 and 3 are Prime Factors common to the Prime Factorizations of 48 and 72

Determine the least number of occurrences of 2 and 3 among the Prime Factorizations:

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

As a result, the Greatest Common Factor (GCF) of 48 and 72 is equal to 2 x 2 x 2 x 3, which equals the product of 2 and 3 raised to the powers of their least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF(48, 72) = 2³ x 3¹ = 2 x 2 x 2 x 3
• GCF(48, 72) = 8 x 3
• GCF(48, 72) = 24

Therefore, the Greatest Common Factor of 48 and 72 by Prime Factorization = 24