What is the Greatest Common Factor of 6304 and 6314?

Greatest common factor (GCF) of 6304 and 6314 is 2.

GCF(6304,6314) = 2

We will now calculate the prime factors of 6304 and 6314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6304 and 6314.

How to find the GCF of 6304 and 6314?

We will first find the prime factorization of 6304 and 6314. After we will calculate the factors of 6304 and 6314 and find the biggest common factor number .

Step-1: Prime Factorization of 6304

Prime factors of 6304 are 2, 197. Prime factorization of 6304 in exponential form is:

6304 = 2⁵ × 197¹

Step-2: 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-3: Factors of 6304

List of positive integer factors of 6304 that divides 6304 without a remainder.

1, 2, 4, 8, 16, 32, 197, 394, 788, 1576, 3152

Step-4: Factors of 6314

List of positive integer factors of 6314 that divides 6304 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6304 and 6314. The biggest common factor number is the GCF number.
So the greatest common factor 6304 and 6314 is 2.

Also check out the Least Common Multiple of 6304 and 6314