What is the Greatest Common Factor of 75189 and 75205?

Greatest common factor (GCF) of 75189 and 75205 is 1.

GCF(75189,75205) = 1

We will now calculate the prime factors of 75189 and 75205, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75189 and 75205.

How to find the GCF of 75189 and 75205?

We will first find the prime factorization of 75189 and 75205. After we will calculate the factors of 75189 and 75205 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 75205

Prime factors of 75205 are 5, 13, 89. Prime factorization of 75205 in exponential form is:

75205 = 5¹ × 13² × 89¹

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 75205

List of positive integer factors of 75205 that divides 75189 without a remainder.

1, 5, 13, 65, 89, 169, 445, 845, 1157, 5785, 15041

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75189 and 75205. The biggest common factor number is the GCF number.
So the greatest common factor 75189 and 75205 is 1.

Also check out the Least Common Multiple of 75189 and 75205