What is the Greatest Common Factor of 75204 and 75222?

Greatest common factor (GCF) of 75204 and 75222 is 18.

GCF(75204,75222) = 18

We will now calculate the prime factors of 75204 and 75222, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75204 and 75222.

How to find the GCF of 75204 and 75222?

We will first find the prime factorization of 75204 and 75222. After we will calculate the factors of 75204 and 75222 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 75222

Prime factors of 75222 are 2, 3, 7, 199. Prime factorization of 75222 in exponential form is:

75222 = 2¹ × 3³ × 7¹ × 199¹

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 75222

List of positive integer factors of 75222 that divides 75204 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 199, 378, 398, 597, 1194, 1393, 1791, 2786, 3582, 4179, 5373, 8358, 10746, 12537, 25074, 37611

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75204 and 75222. The biggest common factor number is the GCF number.
So the greatest common factor 75204 and 75222 is 18.

Also check out the Least Common Multiple of 75204 and 75222