What is the Greatest Common Factor of 2000 and 2010?

Greatest common factor (GCF) of 2000 and 2010 is 10.

GCF(2000,2010) = 10

We will now calculate the prime factors of 2000 and 2010, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2000 and 2010.

How to find the GCF of 2000 and 2010?

We will first find the prime factorization of 2000 and 2010. After we will calculate the factors of 2000 and 2010 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 2010

Prime factors of 2010 are 2, 3, 5, 67. Prime factorization of 2010 in exponential form is:

2010 = 2¹ × 3¹ × 5¹ × 67¹

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 2010

List of positive integer factors of 2010 that divides 2000 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2000 and 2010. The biggest common factor number is the GCF number.
So the greatest common factor 2000 and 2010 is 10.

Also check out the Least Common Multiple of 2000 and 2010