What is the Greatest Common Factor of 75165 and 75174?

Greatest common factor (GCF) of 75165 and 75174 is 3.

GCF(75165,75174) = 3

We will now calculate the prime factors of 75165 and 75174, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75165 and 75174.

How to find the GCF of 75165 and 75174?

We will first find the prime factorization of 75165 and 75174. After we will calculate the factors of 75165 and 75174 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 75174

Prime factors of 75174 are 2, 3, 11, 17, 67. Prime factorization of 75174 in exponential form is:

75174 = 2¹ × 3¹ × 11¹ × 17¹ × 67¹

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 75174

List of positive integer factors of 75174 that divides 75165 without a remainder.

1, 2, 3, 6, 11, 17, 22, 33, 34, 51, 66, 67, 102, 134, 187, 201, 374, 402, 561, 737, 1122, 1139, 1474, 2211, 2278, 3417, 4422, 6834, 12529, 25058, 37587

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75165 and 75174. The biggest common factor number is the GCF number.
So the greatest common factor 75165 and 75174 is 3.

Also check out the Least Common Multiple of 75165 and 75174