What is the Greatest Common Factor of 75189 and 75198?

Greatest common factor (GCF) of 75189 and 75198 is 3.

GCF(75189,75198) = 3

We will now calculate the prime factors of 75189 and 75198, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75189 and 75198.

How to find the GCF of 75189 and 75198?

We will first find the prime factorization of 75189 and 75198. After we will calculate the factors of 75189 and 75198 and find the biggest common factor number .

Step-1: Prime Factorization of 75189

Prime factors of 75189 are 3, 71, 353. Prime factorization of 75189 in exponential form is:

75189 = 3¹ × 71¹ × 353¹

Step-2: Prime Factorization of 75198

Prime factors of 75198 are 2, 3, 83, 151. Prime factorization of 75198 in exponential form is:

75198 = 2¹ × 3¹ × 83¹ × 151¹

Step-3: Factors of 75189

List of positive integer factors of 75189 that divides 75189 without a remainder.

1, 3, 71, 213, 353, 1059, 25063

Step-4: Factors of 75198

List of positive integer factors of 75198 that divides 75189 without a remainder.

1, 2, 3, 6, 83, 151, 166, 249, 302, 453, 498, 906, 12533, 25066, 37599

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75189 and 75198. The biggest common factor number is the GCF number.
So the greatest common factor 75189 and 75198 is 3.

Also check out the Least Common Multiple of 75189 and 75198