What is the Greatest Common Factor of 75204 and 75219?

Greatest common factor (GCF) of 75204 and 75219 is 3.

GCF(75204,75219) = 3

We will now calculate the prime factors of 75204 and 75219, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75204 and 75219.

How to find the GCF of 75204 and 75219?

We will first find the prime factorization of 75204 and 75219. After we will calculate the factors of 75204 and 75219 and find the biggest common factor number .

Step-1: Prime Factorization of 75204

Prime factors of 75204 are 2, 3, 2089. Prime factorization of 75204 in exponential form is:

75204 = 2² × 3² × 2089¹

Step-2: Prime Factorization of 75219

Prime factors of 75219 are 3, 25073. Prime factorization of 75219 in exponential form is:

75219 = 3¹ × 25073¹

Step-3: Factors of 75204

List of positive integer factors of 75204 that divides 75204 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 2089, 4178, 6267, 8356, 12534, 18801, 25068, 37602

Step-4: Factors of 75219

List of positive integer factors of 75219 that divides 75204 without a remainder.

1, 3, 25073

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75204 and 75219. The biggest common factor number is the GCF number.
So the greatest common factor 75204 and 75219 is 3.

Also check out the Least Common Multiple of 75204 and 75219