What is the Greatest Common Factor of 2000 and 2007?

Greatest common factor (GCF) of 2000 and 2007 is 1.

GCF(2000,2007) = 1

We will now calculate the prime factors of 2000 and 2007, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2000 and 2007.

How to find the GCF of 2000 and 2007?

We will first find the prime factorization of 2000 and 2007. After we will calculate the factors of 2000 and 2007 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 2007

Prime factors of 2007 are 3, 223. Prime factorization of 2007 in exponential form is:

2007 = 3² × 223¹

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 2007

List of positive integer factors of 2007 that divides 2000 without a remainder.

1, 3, 9, 223, 669

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2000 and 2007. The biggest common factor number is the GCF number.
So the greatest common factor 2000 and 2007 is 1.

Also check out the Least Common Multiple of 2000 and 2007