Greatest Common Factor of 6 and 10 by Prime Factorization

Given Numbers: 6, 10
Identify the Prime Factors of 6 and 10 by Prime Factorization

• Prime Factorization of 6: 6 = 2 x 3 = 2¹ x 3¹
• Prime Factorization of 10: 10 = 2 x 5 = 2¹ x 5¹

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 6 and 10

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

• 2 occurs 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 6 and 10 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 (6, 10) = 2¹
• GCF(6, 10) = 2

Therefore, the Greatest Common Factor of 6 and 10 by Prime Factorization = 2