What is the Greatest Common Factor of 13857 and 13869?

Greatest common factor (GCF) of 13857 and 13869 is 3.

GCF(13857,13869) = 3

We will now calculate the prime factors of 13857 and 13869, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13857 and 13869.

How to find the GCF of 13857 and 13869?

We will first find the prime factorization of 13857 and 13869. After we will calculate the factors of 13857 and 13869 and find the biggest common factor number .

Step-1: Prime Factorization of 13857

Prime factors of 13857 are 3, 31, 149. Prime factorization of 13857 in exponential form is:

13857 = 3¹ × 31¹ × 149¹

Step-2: Prime Factorization of 13869

Prime factors of 13869 are 3, 23, 67. Prime factorization of 13869 in exponential form is:

13869 = 3² × 23¹ × 67¹

Step-3: Factors of 13857

List of positive integer factors of 13857 that divides 13857 without a remainder.

1, 3, 31, 93, 149, 447, 4619

Step-4: Factors of 13869

List of positive integer factors of 13869 that divides 13857 without a remainder.

1, 3, 9, 23, 67, 69, 201, 207, 603, 1541, 4623

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13857 and 13869. The biggest common factor number is the GCF number.
So the greatest common factor 13857 and 13869 is 3.

Also check out the Least Common Multiple of 13857 and 13869