What is the Greatest Common Factor of 31314 and 31323?

Greatest common factor (GCF) of 31314 and 31323 is 3.

GCF(31314,31323) = 3

We will now calculate the prime factors of 31314 and 31323, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31314 and 31323.

How to find the GCF of 31314 and 31323?

We will first find the prime factorization of 31314 and 31323. After we will calculate the factors of 31314 and 31323 and find the biggest common factor number .

Step-1: Prime Factorization of 31314

Prime factors of 31314 are 2, 3, 17, 307. Prime factorization of 31314 in exponential form is:

31314 = 2¹ × 3¹ × 17¹ × 307¹

Step-2: Prime Factorization of 31323

Prime factors of 31323 are 3, 53, 197. Prime factorization of 31323 in exponential form is:

31323 = 3¹ × 53¹ × 197¹

Step-3: Factors of 31314

List of positive integer factors of 31314 that divides 31314 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 307, 614, 921, 1842, 5219, 10438, 15657

Step-4: Factors of 31323

List of positive integer factors of 31323 that divides 31314 without a remainder.

1, 3, 53, 159, 197, 591, 10441

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31314 and 31323. The biggest common factor number is the GCF number.
So the greatest common factor 31314 and 31323 is 3.

Also check out the Least Common Multiple of 31314 and 31323