What is the Greatest Common Factor of 13878 and 13884?

Greatest common factor (GCF) of 13878 and 13884 is 6.

GCF(13878,13884) = 6

We will now calculate the prime factors of 13878 and 13884, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13878 and 13884.

How to find the GCF of 13878 and 13884?

We will first find the prime factorization of 13878 and 13884. After we will calculate the factors of 13878 and 13884 and find the biggest common factor number .

Step-1: Prime Factorization of 13878

Prime factors of 13878 are 2, 3, 257. Prime factorization of 13878 in exponential form is:

13878 = 2¹ × 3³ × 257¹

Step-2: Prime Factorization of 13884

Prime factors of 13884 are 2, 3, 13, 89. Prime factorization of 13884 in exponential form is:

13884 = 2² × 3¹ × 13¹ × 89¹

Step-3: Factors of 13878

List of positive integer factors of 13878 that divides 13878 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 257, 514, 771, 1542, 2313, 4626, 6939

Step-4: Factors of 13884

List of positive integer factors of 13884 that divides 13878 without a remainder.

1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 89, 156, 178, 267, 356, 534, 1068, 1157, 2314, 3471, 4628, 6942

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13878 and 13884. The biggest common factor number is the GCF number.
So the greatest common factor 13878 and 13884 is 6.

Also check out the Least Common Multiple of 13878 and 13884