What is the Greatest Common Factor of 13966 and 13986?

Greatest common factor (GCF) of 13966 and 13986 is 2.

GCF(13966,13986) = 2

We will now calculate the prime factors of 13966 and 13986, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13966 and 13986.

How to find the GCF of 13966 and 13986?

We will first find the prime factorization of 13966 and 13986. After we will calculate the factors of 13966 and 13986 and find the biggest common factor number .

Step-1: Prime Factorization of 13966

Prime factors of 13966 are 2, 6983. Prime factorization of 13966 in exponential form is:

13966 = 2¹ × 6983¹

Step-2: Prime Factorization of 13986

Prime factors of 13986 are 2, 3, 7, 37. Prime factorization of 13986 in exponential form is:

13986 = 2¹ × 3³ × 7¹ × 37¹

Step-3: Factors of 13966

List of positive integer factors of 13966 that divides 13966 without a remainder.

1, 2, 6983

Step-4: Factors of 13986

List of positive integer factors of 13986 that divides 13966 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 37, 42, 54, 63, 74, 111, 126, 189, 222, 259, 333, 378, 518, 666, 777, 999, 1554, 1998, 2331, 4662, 6993

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13966 and 13986. The biggest common factor number is the GCF number.
So the greatest common factor 13966 and 13986 is 2.

Also check out the Least Common Multiple of 13966 and 13986