What is the Greatest Common Factor of 13986 and 14000?

Greatest common factor (GCF) of 13986 and 14000 is 14.

GCF(13986,14000) = 14

We will now calculate the prime factors of 13986 and 14000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13986 and 14000.

How to find the GCF of 13986 and 14000?

We will first find the prime factorization of 13986 and 14000. After we will calculate the factors of 13986 and 14000 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 14000

Prime factors of 14000 are 2, 5, 7. Prime factorization of 14000 in exponential form is:

14000 = 2⁴ × 5³ × 7¹

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 14000

List of positive integer factors of 14000 that divides 13986 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 125, 140, 175, 200, 250, 280, 350, 400, 500, 560, 700, 875, 1000, 1400, 1750, 2000, 2800, 3500, 7000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13986 and 14000. The biggest common factor number is the GCF number.
So the greatest common factor 13986 and 14000 is 14.

Also check out the Least Common Multiple of 13986 and 14000