What is the Greatest Common Factor of 2000 and 2009?

Greatest common factor (GCF) of 2000 and 2009 is 1.

GCF(2000,2009) = 1

We will now calculate the prime factors of 2000 and 2009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2000 and 2009.

How to find the GCF of 2000 and 2009?

We will first find the prime factorization of 2000 and 2009. After we will calculate the factors of 2000 and 2009 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 2009

Prime factors of 2009 are 7, 41. Prime factorization of 2009 in exponential form is:

2009 = 7² × 41¹

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 2009

List of positive integer factors of 2009 that divides 2000 without a remainder.

1, 7, 41, 49, 287

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2000 and 2009. The biggest common factor number is the GCF number.
So the greatest common factor 2000 and 2009 is 1.

Also check out the Least Common Multiple of 2000 and 2009