What is the Greatest Common Factor of 8000 and 8004?

Greatest common factor (GCF) of 8000 and 8004 is 4.

GCF(8000,8004) = 4

We will now calculate the prime factors of 8000 and 8004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 8000 and 8004.

How to find the GCF of 8000 and 8004?

We will first find the prime factorization of 8000 and 8004. After we will calculate the factors of 8000 and 8004 and find the biggest common factor number .

Step-1: Prime Factorization of 8000

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

8000 = 2⁶ × 5³

Step-2: Prime Factorization of 8004

Prime factors of 8004 are 2, 3, 23, 29. Prime factorization of 8004 in exponential form is:

8004 = 2² × 3¹ × 23¹ × 29¹

Step-3: Factors of 8000

List of positive integer factors of 8000 that divides 8000 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

Step-4: Factors of 8004

List of positive integer factors of 8004 that divides 8000 without a remainder.

1, 2, 3, 4, 6, 12, 23, 29, 46, 58, 69, 87, 92, 116, 138, 174, 276, 348, 667, 1334, 2001, 2668, 4002

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 8000 and 8004. The biggest common factor number is the GCF number.
So the greatest common factor 8000 and 8004 is 4.

Also check out the Least Common Multiple of 8000 and 8004