Greatest Common Factor of 21, 28 and 32 by Prime Factorization

Given Numbers: 21, 28, 32
Identify the Prime Factors of 21, 28 and 32 by Prime Factorization

• Prime Factorization of 21: 21 = 3 x 7 = 3¹ x 7¹
• Prime Factorization of 28: 28 = 2 x 2 x 7 = 2² x 7¹
• Prime Factorization of 32: 32 = 2 x 2 x 2 x 2 x 2 = 2⁵

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

• There are no Prime Factors common to the Prime Factorizations of 21, 28 and 32

Therefore, the Greatest Common Factor of 21, 28 and 32 = 1
Note: Since the GCF(21, 28, 32) = 1, as a set, {21, 28, 32} are coprime