What is the Greatest Common Factor of 14365 and 14382?

Greatest common factor (GCF) of 14365 and 14382 is 17.

GCF(14365,14382) = 17

We will now calculate the prime factors of 14365 and 14382, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14365 and 14382.

How to find the GCF of 14365 and 14382?

We will first find the prime factorization of 14365 and 14382. After we will calculate the factors of 14365 and 14382 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 14382

Prime factors of 14382 are 2, 3, 17, 47. Prime factorization of 14382 in exponential form is:

14382 = 2¹ × 3² × 17¹ × 47¹

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 14382

List of positive integer factors of 14382 that divides 14365 without a remainder.

1, 2, 3, 6, 9, 17, 18, 34, 47, 51, 94, 102, 141, 153, 282, 306, 423, 799, 846, 1598, 2397, 4794, 7191

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14365 and 14382. The biggest common factor number is the GCF number.
So the greatest common factor 14365 and 14382 is 17.

Also check out the Least Common Multiple of 14365 and 14382