What is the Greatest Common Factor of 2000 and 2005?

Greatest common factor (GCF) of 2000 and 2005 is 5.

GCF(2000,2005) = 5

We will now calculate the prime factors of 2000 and 2005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2000 and 2005.

How to find the GCF of 2000 and 2005?

We will first find the prime factorization of 2000 and 2005. After we will calculate the factors of 2000 and 2005 and find the biggest common factor number .

Step-1: Prime Factorization of 2000

Prime factors of 2000 are 2, 5. Prime factorization of 2000 in exponential form is:

2000 = 2⁴ × 5³

Step-2: Prime Factorization of 2005

Prime factors of 2005 are 5, 401. Prime factorization of 2005 in exponential form is:

2005 = 5¹ × 401¹

Step-3: Factors of 2000

List of positive integer factors of 2000 that divides 2000 without a remainder.

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

Step-4: Factors of 2005

List of positive integer factors of 2005 that divides 2000 without a remainder.

1, 5, 401

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2000 and 2005. The biggest common factor number is the GCF number.
So the greatest common factor 2000 and 2005 is 5.

Also check out the Least Common Multiple of 2000 and 2005