What is the Greatest Common Factor of 14365 and 14378?

Greatest common factor (GCF) of 14365 and 14378 is 13.

GCF(14365,14378) = 13

We will now calculate the prime factors of 14365 and 14378, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14365 and 14378.

How to find the GCF of 14365 and 14378?

We will first find the prime factorization of 14365 and 14378. After we will calculate the factors of 14365 and 14378 and find the biggest common factor number .

Step-1: Prime Factorization of 14365

Prime factors of 14365 are 5, 13, 17. Prime factorization of 14365 in exponential form is:

14365 = 5¹ × 13² × 17¹

Step-2: Prime Factorization of 14378

Prime factors of 14378 are 2, 7, 13, 79. Prime factorization of 14378 in exponential form is:

14378 = 2¹ × 7¹ × 13¹ × 79¹

Step-3: Factors of 14365

List of positive integer factors of 14365 that divides 14365 without a remainder.

1, 5, 13, 17, 65, 85, 169, 221, 845, 1105, 2873

Step-4: Factors of 14378

List of positive integer factors of 14378 that divides 14365 without a remainder.

1, 2, 7, 13, 14, 26, 79, 91, 158, 182, 553, 1027, 1106, 2054, 7189

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14365 and 14378. The biggest common factor number is the GCF number.
So the greatest common factor 14365 and 14378 is 13.

Also check out the Least Common Multiple of 14365 and 14378