Greatest Common Factor of 2000 and 2005

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 2000, 2005 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 2000 and 2005 is 5.

GCF(2000,2005) = 5

GCF of 2000 and 2005

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

GCF of:
and

Greatest Common Factor of 2000 and 2005

GCF of 2000 and 2005 is 5

Prime Factorization of 2000


2 2000
2 1000
2 500
2 250
5 125
5 25
5 5
1

Prime factors of 2000 are 2,5. Prime factorization of 2000 in exponential form is:

2000 = 24×53

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

∴ So by taking common prime factors GCF of 2000 and 2005 is 5

Greatest Common Factor of 2000 and 2005 by matching factors method

Factors of 2000

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

1,2,4,5,8,10,16,20,25,40,50,80,100,125,200,250,400,500,1000,2000

Factors of 2005

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

1,5,401,2005

Greatest Common Factor

We found the factors and prime factorization of 2000 and 2005. The biggest common factor number is the GCF number.
So the greatest common factor 2000 and 2005 is 5.

Also check out the Least Common Multiple of 2000 and 2005

Properties of GCF 2000 and 2005

(i) The GCF of 2000 and 2005 is associative

GCF of 2000 and 2005 = GCF of 2005 and 2000

Related Greatest Common Factor of 2000

Related Greatest Common Factor of 2005

Frequently Asked Questions on GCF of 2000 and 2005

1. What is the GCF of 2000 and 2005?

Answer: GCF of 2000 and 2005 is 5.

2. What are the Factors of 2000?

Answer: Factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000. There are 20 integers that are factors of 2000. The greatest factor of 2000 is 2000.

3. 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.

4. How to Find the GCF of 2000 and 2005?

Answer:

Greatest Common Factor of 2000 and 2005 = 5

Step 1: Find the prime factorization of 2000

2000 = 2 x 2 x 2 x 2 x 5 x 5 x 5

Step 2: Find the prime factorization of 2005

2005 = 5 x 401

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 2000 and 2005 is 5