What is the Greatest Common Factor of 13300 and 13314?

Greatest common factor (GCF) of 13300 and 13314 is 14.

GCF(13300,13314) = 14

We will now calculate the prime factors of 13300 and 13314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13300 and 13314.

How to find the GCF of 13300 and 13314?

We will first find the prime factorization of 13300 and 13314. After we will calculate the factors of 13300 and 13314 and find the biggest common factor number .

Step-1: Prime Factorization of 13300

Prime factors of 13300 are 2, 5, 7, 19. Prime factorization of 13300 in exponential form is:

13300 = 2² × 5² × 7¹ × 19¹

Step-2: Prime Factorization of 13314

Prime factors of 13314 are 2, 3, 7, 317. Prime factorization of 13314 in exponential form is:

13314 = 2¹ × 3¹ × 7¹ × 317¹

Step-3: Factors of 13300

List of positive integer factors of 13300 that divides 13300 without a remainder.

1, 2, 4, 5, 7, 10, 14, 19, 20, 25, 28, 35, 38, 50, 70, 76, 95, 100, 133, 140, 175, 190, 266, 350, 380, 475, 532, 665, 700, 950, 1330, 1900, 2660, 3325, 6650

Step-4: Factors of 13314

List of positive integer factors of 13314 that divides 13300 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 317, 634, 951, 1902, 2219, 4438, 6657

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13300 and 13314. The biggest common factor number is the GCF number.
So the greatest common factor 13300 and 13314 is 14.

Also check out the Least Common Multiple of 13300 and 13314