What is the Greatest Common Factor of 13842 and 13857?

Greatest common factor (GCF) of 13842 and 13857 is 3.

GCF(13842,13857) = 3

We will now calculate the prime factors of 13842 and 13857, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13842 and 13857.

How to find the GCF of 13842 and 13857?

We will first find the prime factorization of 13842 and 13857. After we will calculate the factors of 13842 and 13857 and find the biggest common factor number .

Step-1: Prime Factorization of 13842

Prime factors of 13842 are 2, 3, 769. Prime factorization of 13842 in exponential form is:

13842 = 2¹ × 3² × 769¹

Step-2: 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-3: Factors of 13842

List of positive integer factors of 13842 that divides 13842 without a remainder.

1, 2, 3, 6, 9, 18, 769, 1538, 2307, 4614, 6921

Step-4: Factors of 13857

List of positive integer factors of 13857 that divides 13842 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13842 and 13857. The biggest common factor number is the GCF number.
So the greatest common factor 13842 and 13857 is 3.

Also check out the Least Common Multiple of 13842 and 13857