What is the Greatest Common Factor of 75165 and 75180?

Greatest common factor (GCF) of 75165 and 75180 is 15.

GCF(75165,75180) = 15

We will now calculate the prime factors of 75165 and 75180, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75165 and 75180.

How to find the GCF of 75165 and 75180?

We will first find the prime factorization of 75165 and 75180. After we will calculate the factors of 75165 and 75180 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 75180

Prime factors of 75180 are 2, 3, 5, 7, 179. Prime factorization of 75180 in exponential form is:

75180 = 2² × 3¹ × 5¹ × 7¹ × 179¹

Step-3: Factors of 75165

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

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

Step-4: Factors of 75180

List of positive integer factors of 75180 that divides 75165 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 179, 210, 358, 420, 537, 716, 895, 1074, 1253, 1790, 2148, 2506, 2685, 3580, 3759, 5012, 5370, 6265, 7518, 10740, 12530, 15036, 18795, 25060, 37590

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75165 and 75180. The biggest common factor number is the GCF number.
So the greatest common factor 75165 and 75180 is 15.

Also check out the Least Common Multiple of 75165 and 75180