Greatest Common Factor of 2005 and 2010

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 2005, 2010 i.e. 5 largest integer by which both the numbers can be divided.

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

GCF(2005,2010) = 5

GCF of 2005 and 2010

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 2005 and 2010

GCF of 2005 and 2010 is 5

Prime Factorization of 2005


5 2005
401 401
1

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

2005 = 51×4011

Prime Factorization of 2010


2 2010
3 1005
5 335
67 67
1

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

2010 = 21×31×51×671

∴ So by taking common prime factors GCF of 2005 and 2010 is 5

Greatest Common Factor of 2005 and 2010 by matching factors method

Factors of 2005

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

1,5,401,2005

Factors of 2010

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

1,2,3,5,6,10,15,30,67,134,201,335,402,670,1005,2010

Greatest Common Factor

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

Properties of GCF 2005 and 2010

(i) The GCF of 2005 and 2010 is associative

GCF of 2005 and 2010 = GCF of 2010 and 2005

Related Greatest Common Factor of 2005

Related Greatest Common Factor of 2010

Frequently Asked Questions on GCF of 2005 and 2010

1. What is the GCF of 2005 and 2010?

Answer: GCF of 2005 and 2010 is 5.

2. What are the Factors of 2005?

Answer: Factors of 2005 are 1, 5, 401, 2005. There are 4 integers that are factors of 2005. The greatest factor of 2005 is 2005.

3. What are the Factors of 2010?

Answer: Factors of 2010 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010. There are 16 integers that are factors of 2010. The greatest factor of 2010 is 2010.

4. How to Find the GCF of 2005 and 2010?

Answer:

Greatest Common Factor of 2005 and 2010 = 5

Step 1: Find the prime factorization of 2005

2005 = 5 x 401

Step 2: Find the prime factorization of 2010

2010 = 2 x 3 x 5 x 67

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 5

Step 4: Therefore, the greatest common factor of 2005 and 2010 is 5