What is the Greatest Common Factor of 4000 and 4008?

Greatest common factor (GCF) of 4000 and 4008 is 8.

GCF(4000,4008) = 8

We will now calculate the prime factors of 4000 and 4008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4000 and 4008.

How to find the GCF of 4000 and 4008?

We will first find the prime factorization of 4000 and 4008. After we will calculate the factors of 4000 and 4008 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 4008

Prime factors of 4008 are 2, 3, 167. Prime factorization of 4008 in exponential form is:

4008 = 2³ × 3¹ × 167¹

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 4008

List of positive integer factors of 4008 that divides 4000 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 167, 334, 501, 668, 1002, 1336, 2004

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 4000 and 4008. The biggest common factor number is the GCF number.
So the greatest common factor 4000 and 4008 is 8.

Also check out the Least Common Multiple of 4000 and 4008