What is the Greatest Common Factor of 4000 and 4004?

Greatest common factor (GCF) of 4000 and 4004 is 4.

GCF(4000,4004) = 4

We will now calculate the prime factors of 4000 and 4004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4000 and 4004.

How to find the GCF of 4000 and 4004?

We will first find the prime factorization of 4000 and 4004. After we will calculate the factors of 4000 and 4004 and find the biggest common factor number .

Step-1: Prime Factorization of 4000

Prime factors of 4000 are 2, 5. Prime factorization of 4000 in exponential form is:

4000 = 2⁵ × 5³

Step-2: Prime Factorization of 4004

Prime factors of 4004 are 2, 7, 11, 13. Prime factorization of 4004 in exponential form is:

4004 = 2² × 7¹ × 11¹ × 13¹

Step-3: Factors of 4000

List of positive integer factors of 4000 that divides 4000 without a remainder.

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

Step-4: Factors of 4004

List of positive integer factors of 4004 that divides 4000 without a remainder.

1, 2, 4, 7, 11, 13, 14, 22, 26, 28, 44, 52, 77, 91, 143, 154, 182, 286, 308, 364, 572, 1001, 2002

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 4000 and 4004. The biggest common factor number is the GCF number.
So the greatest common factor 4000 and 4004 is 4.

Also check out the Least Common Multiple of 4000 and 4004