What is the Greatest Common Factor of 2005 and 2010?

Greatest common factor (GCF) of 2005 and 2010 is 5.

GCF(2005,2010) = 5

We will now calculate the prime factors of 2005 and 2010, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2005 and 2010.

How to find the GCF of 2005 and 2010?

We will first find the prime factorization of 2005 and 2010. After we will calculate the factors of 2005 and 2010 and find the biggest common factor number .

Step-1: Prime Factorization of 2005

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

2005 = 5¹ × 401¹

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 2005

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

1, 5, 401

Step-4: Factors of 2010

List of positive integer factors of 2010 that divides 2005 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 2005 and 2010. The biggest common factor number is the GCF number.
So the greatest common factor 2005 and 2010 is 5.

Also check out the Least Common Multiple of 2005 and 2010