Greatest Common Factor of 14, 20 and 56 by Prime Factorization

Given Numbers: 14, 20, 56
Identify the Prime Factors of 14, 20 and 56 by Prime Factorization

• Prime Factorization of 14: 14 = 2 x 7 = 2¹ x 7¹
• Prime Factorization of 20: 20 = 2 x 2 x 5 = 2² x 5¹
• Prime Factorization of 56: 56 = 2 x 2 x 2 x 7 = 2³ x 7¹

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 14, 20 and 56

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

• 2 occurs at least 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 14, 20 and 56 is equal to 2, which equals 2 raised to the power of its least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF(14, 20, 56) = 2¹
• GCF(14, 20, 56) = 2

Therefore, the Greatest Common Factor of 14, 20 and 56 by Prime Factorization = 2