What is the Greatest Common Factor of 13854 and 13872?

Greatest common factor (GCF) of 13854 and 13872 is 6.

GCF(13854,13872) = 6

We will now calculate the prime factors of 13854 and 13872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13854 and 13872.

How to find the GCF of 13854 and 13872?

We will first find the prime factorization of 13854 and 13872. After we will calculate the factors of 13854 and 13872 and find the biggest common factor number .

Step-1: Prime Factorization of 13854

Prime factors of 13854 are 2, 3, 2309. Prime factorization of 13854 in exponential form is:

13854 = 2¹ × 3¹ × 2309¹

Step-2: Prime Factorization of 13872

Prime factors of 13872 are 2, 3, 17. Prime factorization of 13872 in exponential form is:

13872 = 2⁴ × 3¹ × 17²

Step-3: Factors of 13854

List of positive integer factors of 13854 that divides 13854 without a remainder.

1, 2, 3, 6, 2309, 4618, 6927

Step-4: Factors of 13872

List of positive integer factors of 13872 that divides 13854 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 289, 408, 578, 816, 867, 1156, 1734, 2312, 3468, 4624, 6936

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13854 and 13872. The biggest common factor number is the GCF number.
So the greatest common factor 13854 and 13872 is 6.

Also check out the Least Common Multiple of 13854 and 13872