Greatest Common Factor of 16 and 48 by Prime Factorization

Given Numbers: 16, 48
Identify the Prime Factors of 16 and 48 by Prime Factorization

• Prime Factorization of 16: 16 = 2 x 2 x 2 x 2 = 2⁴
• Prime Factorization of 48: 48 = 2 x 2 x 2 x 2 x 3 = 2⁴ x 3¹

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 16 and 48

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

• 2 occurs 4 times in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 16 and 48 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(16, 48) = 2⁴ = 2 x 2 x 2 x 2
• GCF(16, 48) = 16

Therefore, the Greatest Common Factor of 16 and 48 by Prime Factorization = 16