What is the Greatest Common Factor of 10304 and 10314?

Greatest common factor (GCF) of 10304 and 10314 is 2.

GCF(10304,10314) = 2

We will now calculate the prime factors of 10304 and 10314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10304 and 10314.

How to find the GCF of 10304 and 10314?

We will first find the prime factorization of 10304 and 10314. After we will calculate the factors of 10304 and 10314 and find the biggest common factor number .

Step-1: Prime Factorization of 10304

Prime factors of 10304 are 2, 7, 23. Prime factorization of 10304 in exponential form is:

10304 = 2⁶ × 7¹ × 23¹

Step-2: Prime Factorization of 10314

Prime factors of 10314 are 2, 3, 191. Prime factorization of 10314 in exponential form is:

10314 = 2¹ × 3³ × 191¹

Step-3: Factors of 10304

List of positive integer factors of 10304 that divides 10304 without a remainder.

1, 2, 4, 7, 8, 14, 16, 23, 28, 32, 46, 56, 64, 92, 112, 161, 184, 224, 322, 368, 448, 644, 736, 1288, 1472, 2576, 5152

Step-4: Factors of 10314

List of positive integer factors of 10314 that divides 10304 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 191, 382, 573, 1146, 1719, 3438, 5157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10304 and 10314. The biggest common factor number is the GCF number.
So the greatest common factor 10304 and 10314 is 2.

Also check out the Least Common Multiple of 10304 and 10314