What is the Greatest Common Factor of 7984 and 8004?

Greatest common factor (GCF) of 7984 and 8004 is 4.

GCF(7984,8004) = 4

We will now calculate the prime factors of 7984 and 8004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7984 and 8004.

How to find the GCF of 7984 and 8004?

We will first find the prime factorization of 7984 and 8004. After we will calculate the factors of 7984 and 8004 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 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 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 8004

List of positive integer factors of 8004 that divides 7984 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 7984 and 8004. The biggest common factor number is the GCF number.
So the greatest common factor 7984 and 8004 is 4.

Also check out the Least Common Multiple of 7984 and 8004