What is the Greatest Common Factor of 13986 and 13993?

Greatest common factor (GCF) of 13986 and 13993 is 7.

GCF(13986,13993) = 7

We will now calculate the prime factors of 13986 and 13993, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13986 and 13993.

How to find the GCF of 13986 and 13993?

We will first find the prime factorization of 13986 and 13993. After we will calculate the factors of 13986 and 13993 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 13993

Prime factors of 13993 are 7, 1999. Prime factorization of 13993 in exponential form is:

13993 = 7¹ × 1999¹

Step-3: Factors of 13986

List of positive integer factors of 13986 that divides 13986 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

Step-4: Factors of 13993

List of positive integer factors of 13993 that divides 13986 without a remainder.

1, 7, 1999

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13986 and 13993. The biggest common factor number is the GCF number.
So the greatest common factor 13986 and 13993 is 7.

Also check out the Least Common Multiple of 13986 and 13993