What is the Greatest Common Factor of 31209 and 31214?

Greatest common factor (GCF) of 31209 and 31214 is 1.

GCF(31209,31214) = 1

We will now calculate the prime factors of 31209 and 31214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31209 and 31214.

How to find the GCF of 31209 and 31214?

We will first find the prime factorization of 31209 and 31214. After we will calculate the factors of 31209 and 31214 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31214

Prime factors of 31214 are 2, 15607. Prime factorization of 31214 in exponential form is:

31214 = 2¹ × 15607¹

Step-3: Factors of 31209

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

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

Step-4: Factors of 31214

List of positive integer factors of 31214 that divides 31209 without a remainder.

1, 2, 15607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31209 and 31214. The biggest common factor number is the GCF number.
So the greatest common factor 31209 and 31214 is 1.

Also check out the Least Common Multiple of 31209 and 31214