What is the Greatest Common Factor of 13800 and 13817?

Greatest common factor (GCF) of 13800 and 13817 is 1.

GCF(13800,13817) = 1

We will now calculate the prime factors of 13800 and 13817, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13800 and 13817.

How to find the GCF of 13800 and 13817?

We will first find the prime factorization of 13800 and 13817. After we will calculate the factors of 13800 and 13817 and find the biggest common factor number .

Step-1: Prime Factorization of 13800

Prime factors of 13800 are 2, 3, 5, 23. Prime factorization of 13800 in exponential form is:

13800 = 2³ × 3¹ × 5² × 23¹

Step-2: Prime Factorization of 13817

Prime factors of 13817 are 41, 337. Prime factorization of 13817 in exponential form is:

13817 = 41¹ × 337¹

Step-3: Factors of 13800

List of positive integer factors of 13800 that divides 13800 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 23, 24, 25, 30, 40, 46, 50, 60, 69, 75, 92, 100, 115, 120, 138, 150, 184, 200, 230, 276, 300, 345, 460, 552, 575, 600, 690, 920, 1150, 1380, 1725, 2300, 2760, 3450, 4600, 6900

Step-4: Factors of 13817

List of positive integer factors of 13817 that divides 13800 without a remainder.

1, 41, 337

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13800 and 13817. The biggest common factor number is the GCF number.
So the greatest common factor 13800 and 13817 is 1.

Also check out the Least Common Multiple of 13800 and 13817