Greatest Common Factor of 21 and 35 by Prime Factorization

Given Numbers: 21, 35
Identify the Prime Factors of 21 and 35 by Prime Factorization

• Prime Factorization of 21: 21 = 3 x 7 = 3¹ x 7¹
• Prime Factorization of 35: 35 = 5 x 7 = 5¹ x 7¹

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

• 7 is the only Prime Factor common to the Prime Factorizations of 21 and 35

Determine the least number of occurrences of 7 among the Prime Factorizations:

• 7 occurs 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 21 and 35 is equal to 7, which equals 7 raised to the power of its least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF (21, 35) = 7¹
• GCF(21, 35) = 7

Therefore, the Greatest Common Factor of 21 and 35 by Prime Factorization = 7