What is the Greatest Common Factor of 10314 and 10330?

Greatest common factor (GCF) of 10314 and 10330 is 2.

GCF(10314,10330) = 2

We will now calculate the prime factors of 10314 and 10330, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10314 and 10330.

How to find the GCF of 10314 and 10330?

We will first find the prime factorization of 10314 and 10330. After we will calculate the factors of 10314 and 10330 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 10330

Prime factors of 10330 are 2, 5, 1033. Prime factorization of 10330 in exponential form is:

10330 = 2¹ × 5¹ × 1033¹

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 10330

List of positive integer factors of 10330 that divides 10314 without a remainder.

1, 2, 5, 10, 1033, 2066, 5165

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10314 and 10330. The biggest common factor number is the GCF number.
So the greatest common factor 10314 and 10330 is 2.

Also check out the Least Common Multiple of 10314 and 10330