What is the Greatest Common Factor of 10314 and 10320?

Greatest common factor (GCF) of 10314 and 10320 is 6.

GCF(10314,10320) = 6

We will now calculate the prime factors of 10314 and 10320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10314 and 10320.

How to find the GCF of 10314 and 10320?

We will first find the prime factorization of 10314 and 10320. After we will calculate the factors of 10314 and 10320 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 10320

Prime factors of 10320 are 2, 3, 5, 43. Prime factorization of 10320 in exponential form is:

10320 = 2⁴ × 3¹ × 5¹ × 43¹

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 10320

List of positive integer factors of 10320 that divides 10314 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 43, 48, 60, 80, 86, 120, 129, 172, 215, 240, 258, 344, 430, 516, 645, 688, 860, 1032, 1290, 1720, 2064, 2580, 3440, 5160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10314 and 10320. The biggest common factor number is the GCF number.
So the greatest common factor 10314 and 10320 is 6.

Also check out the Least Common Multiple of 10314 and 10320