What is the Greatest Common Factor of 31194 and 31209?

Greatest common factor (GCF) of 31194 and 31209 is 3.

GCF(31194,31209) = 3

We will now calculate the prime factors of 31194 and 31209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31194 and 31209.

How to find the GCF of 31194 and 31209?

We will first find the prime factorization of 31194 and 31209. After we will calculate the factors of 31194 and 31209 and find the biggest common factor number .

Step-1: Prime Factorization of 31194

Prime factors of 31194 are 2, 3, 1733. Prime factorization of 31194 in exponential form is:

31194 = 2¹ × 3² × 1733¹

Step-2: Prime Factorization of 31209

Prime factors of 31209 are 3, 101, 103. Prime factorization of 31209 in exponential form is:

31209 = 3¹ × 101¹ × 103¹

Step-3: Factors of 31194

List of positive integer factors of 31194 that divides 31194 without a remainder.

1, 2, 3, 6, 9, 18, 1733, 3466, 5199, 10398, 15597

Step-4: Factors of 31209

List of positive integer factors of 31209 that divides 31194 without a remainder.

1, 3, 101, 103, 303, 309, 10403

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31194 and 31209. The biggest common factor number is the GCF number.
So the greatest common factor 31194 and 31209 is 3.

Also check out the Least Common Multiple of 31194 and 31209