What is the Greatest Common Factor of 10314 and 10334?

Greatest common factor (GCF) of 10314 and 10334 is 2.

GCF(10314,10334) = 2

We will now calculate the prime factors of 10314 and 10334, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10314 and 10334.

How to find the GCF of 10314 and 10334?

We will first find the prime factorization of 10314 and 10334. After we will calculate the factors of 10314 and 10334 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 10334

Prime factors of 10334 are 2, 5167. Prime factorization of 10334 in exponential form is:

10334 = 2¹ × 5167¹

Step-3: Factors of 10314

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

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

Step-4: Factors of 10334

List of positive integer factors of 10334 that divides 10314 without a remainder.

1, 2, 5167

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10314 and 10334. The biggest common factor number is the GCF number.
So the greatest common factor 10314 and 10334 is 2.

Also check out the Least Common Multiple of 10314 and 10334