What is the Greatest Common Factor of 12986 and 13000?

Greatest common factor (GCF) of 12986 and 13000 is 2.

GCF(12986,13000) = 2

We will now calculate the prime factors of 12986 and 13000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12986 and 13000.

How to find the GCF of 12986 and 13000?

We will first find the prime factorization of 12986 and 13000. After we will calculate the factors of 12986 and 13000 and find the biggest common factor number .

Step-1: Prime Factorization of 12986

Prime factors of 12986 are 2, 43, 151. Prime factorization of 12986 in exponential form is:

12986 = 2¹ × 43¹ × 151¹

Step-2: Prime Factorization of 13000

Prime factors of 13000 are 2, 5, 13. Prime factorization of 13000 in exponential form is:

13000 = 2³ × 5³ × 13¹

Step-3: Factors of 12986

List of positive integer factors of 12986 that divides 12986 without a remainder.

1, 2, 43, 86, 151, 302, 6493

Step-4: Factors of 13000

List of positive integer factors of 13000 that divides 12986 without a remainder.

1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104, 125, 130, 200, 250, 260, 325, 500, 520, 650, 1000, 1300, 1625, 2600, 3250, 6500

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12986 and 13000. The biggest common factor number is the GCF number.
So the greatest common factor 12986 and 13000 is 2.

Also check out the Least Common Multiple of 12986 and 13000