What is the Greatest Common Factor of 13986 and 14003?

Greatest common factor (GCF) of 13986 and 14003 is 1.

GCF(13986,14003) = 1

We will now calculate the prime factors of 13986 and 14003, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13986 and 14003.

How to find the GCF of 13986 and 14003?

We will first find the prime factorization of 13986 and 14003. After we will calculate the factors of 13986 and 14003 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 14003

Prime factors of 14003 are 11, 19, 67. Prime factorization of 14003 in exponential form is:

14003 = 11¹ × 19¹ × 67¹

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 14003

List of positive integer factors of 14003 that divides 13986 without a remainder.

1, 11, 19, 67, 209, 737, 1273

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13986 and 14003. The biggest common factor number is the GCF number.
So the greatest common factor 13986 and 14003 is 1.

Also check out the Least Common Multiple of 13986 and 14003