Greatest Common Factor of 30, 35 and 105 by Prime Factorization

Given Numbers: 30, 35, 105
Identify the Prime Factors of 30, 35 and 105 by Prime Factorization

• Prime Factorization of 30: 30 = 2 x 3 x 5 = 2¹ x 3¹ x 5¹
• Prime Factorization of 35: 35 = 5 x 7 = 5¹ x 7¹
• Prime Factorization of 105: 105 = 3 x 5 x 7 = 3¹ x 5¹ x 7¹

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

• 5 is the only Prime Factor common to the Prime Factorizations of 30, 35 and 105

Determine the least number of occurrences of 5 among the Prime Factorizations:

• 5 occurs 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 30, 35 and 105 is equal to 5, which equals 5 raised to the power of its least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF (30, 35, 105) = 5¹
• GCF(30, 35, 105) = 5

Therefore, the Greatest Common Factor of 30, 35 and 105 by Prime Factorization = 5