What is the Greatest Common Factor of 4000 and 4005?

Greatest common factor (GCF) of 4000 and 4005 is 5.

GCF(4000,4005) = 5

We will now calculate the prime factors of 4000 and 4005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4000 and 4005.

How to find the GCF of 4000 and 4005?

We will first find the prime factorization of 4000 and 4005. After we will calculate the factors of 4000 and 4005 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 4005

Prime factors of 4005 are 3, 5, 89. Prime factorization of 4005 in exponential form is:

4005 = 3² × 5¹ × 89¹

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 4005

List of positive integer factors of 4005 that divides 4000 without a remainder.

1, 3, 5, 9, 15, 45, 89, 267, 445, 801, 1335

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 4000 and 4005. The biggest common factor number is the GCF number.
So the greatest common factor 4000 and 4005 is 5.

Also check out the Least Common Multiple of 4000 and 4005