What is the Greatest Common Factor of 2000 and 2012?

Greatest common factor (GCF) of 2000 and 2012 is 4.

GCF(2000,2012) = 4

We will now calculate the prime factors of 2000 and 2012, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2000 and 2012.

How to find the GCF of 2000 and 2012?

We will first find the prime factorization of 2000 and 2012. After we will calculate the factors of 2000 and 2012 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 2012

Prime factors of 2012 are 2, 503. Prime factorization of 2012 in exponential form is:

2012 = 2² × 503¹

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 2012

List of positive integer factors of 2012 that divides 2000 without a remainder.

1, 2, 4, 503, 1006

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2000 and 2012. The biggest common factor number is the GCF number.
So the greatest common factor 2000 and 2012 is 4.

Also check out the Least Common Multiple of 2000 and 2012