What is the Greatest Common Factor of 75150 and 75165?

Greatest common factor (GCF) of 75150 and 75165 is 15.

GCF(75150,75165) = 15

We will now calculate the prime factors of 75150 and 75165, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75150 and 75165.

How to find the GCF of 75150 and 75165?

We will first find the prime factorization of 75150 and 75165. After we will calculate the factors of 75150 and 75165 and find the biggest common factor number .

Step-1: Prime Factorization of 75150

Prime factors of 75150 are 2, 3, 5, 167. Prime factorization of 75150 in exponential form is:

75150 = 2¹ × 3² × 5² × 167¹

Step-2: Prime Factorization of 75165

Prime factors of 75165 are 3, 5, 5011. Prime factorization of 75165 in exponential form is:

75165 = 3¹ × 5¹ × 5011¹

Step-3: Factors of 75150

List of positive integer factors of 75150 that divides 75150 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 167, 225, 334, 450, 501, 835, 1002, 1503, 1670, 2505, 3006, 4175, 5010, 7515, 8350, 12525, 15030, 25050, 37575

Step-4: Factors of 75165

List of positive integer factors of 75165 that divides 75150 without a remainder.

1, 3, 5, 15, 5011, 15033, 25055

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75150 and 75165. The biggest common factor number is the GCF number.
So the greatest common factor 75150 and 75165 is 15.

Also check out the Least Common Multiple of 75150 and 75165