What is the Greatest Common Factor of 7984 and 8000?

Greatest common factor (GCF) of 7984 and 8000 is 16.

GCF(7984,8000) = 16

We will now calculate the prime factors of 7984 and 8000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7984 and 8000.

How to find the GCF of 7984 and 8000?

We will first find the prime factorization of 7984 and 8000. After we will calculate the factors of 7984 and 8000 and find the biggest common factor number .

Step-1: Prime Factorization of 7984

Prime factors of 7984 are 2, 499. Prime factorization of 7984 in exponential form is:

7984 = 2⁴ × 499¹

Step-2: Prime Factorization of 8000

Prime factors of 8000 are 2, 5. Prime factorization of 8000 in exponential form is:

8000 = 2⁶ × 5³

Step-3: Factors of 7984

List of positive integer factors of 7984 that divides 7984 without a remainder.

1, 2, 4, 8, 16, 499, 998, 1996, 3992

Step-4: Factors of 8000

List of positive integer factors of 8000 that divides 7984 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 320, 400, 500, 800, 1000, 1600, 2000, 4000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7984 and 8000. The biggest common factor number is the GCF number.
So the greatest common factor 7984 and 8000 is 16.

Also check out the Least Common Multiple of 7984 and 8000