What is the Greatest Common Factor of 13986 and 13992?

Greatest common factor (GCF) of 13986 and 13992 is 6.

GCF(13986,13992) = 6

We will now calculate the prime factors of 13986 and 13992, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13986 and 13992.

How to find the GCF of 13986 and 13992?

We will first find the prime factorization of 13986 and 13992. After we will calculate the factors of 13986 and 13992 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 13992

Prime factors of 13992 are 2, 3, 11, 53. Prime factorization of 13992 in exponential form is:

13992 = 2³ × 3¹ × 11¹ × 53¹

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 13992

List of positive integer factors of 13992 that divides 13986 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 53, 66, 88, 106, 132, 159, 212, 264, 318, 424, 583, 636, 1166, 1272, 1749, 2332, 3498, 4664, 6996

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13986 and 13992. The biggest common factor number is the GCF number.
So the greatest common factor 13986 and 13992 is 6.

Also check out the Least Common Multiple of 13986 and 13992