Greatest Common Factor of 22, 34 and 840 by Prime Factorization

Given Numbers: 22, 34, 840
Identify the Prime Factors of 22, 34 and 840 by Prime Factorization

• Prime Factorization of 22: 22 = 2 x 11 = 2¹ x 11¹
• Prime Factorization of 34: 34 = 2 x 17 = 2¹ x 17¹
• Prime Factorization of 840: 840 = 2 x 2 x 2 x 3 x 5 x 7 = 2³ x 3¹ x 5¹ 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 22, 34 and 840

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 22, 34 and 840 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 (22, 34, 840) = 2¹
• GCF(22, 34, 840) = 2

Therefore, the Greatest Common Factor of 22, 34 and 840 by Prime Factorization = 2