What is the Greatest Common Factor of 6314 and 6321?

Greatest common factor (GCF) of 6314 and 6321 is 7.

GCF(6314,6321) = 7

We will now calculate the prime factors of 6314 and 6321, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6314 and 6321.

How to find the GCF of 6314 and 6321?

We will first find the prime factorization of 6314 and 6321. After we will calculate the factors of 6314 and 6321 and find the biggest common factor number .

Step-1: Prime Factorization of 6314

Prime factors of 6314 are 2, 7, 11, 41. Prime factorization of 6314 in exponential form is:

6314 = 2¹ × 7¹ × 11¹ × 41¹

Step-2: Prime Factorization of 6321

Prime factors of 6321 are 3, 7, 43. Prime factorization of 6321 in exponential form is:

6321 = 3¹ × 7² × 43¹

Step-3: Factors of 6314

List of positive integer factors of 6314 that divides 6314 without a remainder.

1, 2, 7, 11, 14, 22, 41, 77, 82, 154, 287, 451, 574, 902, 3157

Step-4: Factors of 6321

List of positive integer factors of 6321 that divides 6314 without a remainder.

1, 3, 7, 21, 43, 49, 129, 147, 301, 903, 2107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6314 and 6321. The biggest common factor number is the GCF number.
So the greatest common factor 6314 and 6321 is 7.

Also check out the Least Common Multiple of 6314 and 6321