Greatest Common Factor of 75, 90, 120, 135 and 150 by Prime Factorization

Given Numbers: 75, 90, 120, 135, 150
Identify the Prime Factors of 75, 90, 120, 135 and 150 by Prime Factorization

• Prime Factorization of 75: 75 = 3 x 5 x 5 = 3¹ x 5²
• Prime Factorization of 90: 90 = 2 x 3 x 3 x 5 = 2¹ x 3² x 5¹
• Prime Factorization of 120: 120 = 2 x 2 x 2 x 3 x 5 = 2³ x 3¹ x 5¹
• Prime Factorization of 135: 135 = 3 x 3 x 3 x 5 = 3³ x 5¹
• Prime Factorization of 150: 150 = 2 x 3 x 5 x 5 = 2¹ x 3¹ x 5²

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

• 3 and 5 are Prime Factors common to the Prime Factorizations of 75, 90, 120, 135 and 150

Determine the least number of occurrences of 3 and 5 among the Prime Factorizations:

• 3 occurs at least 1 time in each Prime Factorization
• 5 occurs at least 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 75, 90, 120, 135 and 150 is equal to 3 x 5, which equals the product of 3 and 5 raised to the powers of their least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF(75, 90, 120, 135, 150) = 3¹ x 5¹
• GCF(75, 90, 120, 135, 150) = 3 x 5
• GCF(75, 90, 120, 135, 150) = 15

Therefore, the Greatest Common Factor of 75, 90, 120, 135 and 150 by Prime Factorization = 15