What is the Greatest Common Factor of 6986 and 7000?

Greatest common factor (GCF) of 6986 and 7000 is 14.

GCF(6986,7000) = 14

We will now calculate the prime factors of 6986 and 7000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6986 and 7000.

How to find the GCF of 6986 and 7000?

We will first find the prime factorization of 6986 and 7000. After we will calculate the factors of 6986 and 7000 and find the biggest common factor number .

Step-1: Prime Factorization of 6986

Prime factors of 6986 are 2, 7, 499. Prime factorization of 6986 in exponential form is:

6986 = 2¹ × 7¹ × 499¹

Step-2: Prime Factorization of 7000

Prime factors of 7000 are 2, 5, 7. Prime factorization of 7000 in exponential form is:

7000 = 2³ × 5³ × 7¹

Step-3: Factors of 6986

List of positive integer factors of 6986 that divides 6986 without a remainder.

1, 2, 7, 14, 499, 998, 3493

Step-4: Factors of 7000

List of positive integer factors of 7000 that divides 6986 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6986 and 7000. The biggest common factor number is the GCF number.
So the greatest common factor 6986 and 7000 is 14.

Also check out the Least Common Multiple of 6986 and 7000