Greatest Common Factor of 2000 and 2006

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, 2006 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 2000 and 2006 is 2.

GCF(2000,2006) = 2

GCF of 2000 and 2006

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

GCF of:
and

Greatest Common Factor of 2000 and 2006

GCF of 2000 and 2006 is 2

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 2006


2 2006
17 1003
59 59
1

Prime factors of 2006 are 2,17,59. Prime factorization of 2006 in exponential form is:

2006 = 21×171×591

∴ So by taking common prime factors GCF of 2000 and 2006 is 2

Greatest Common Factor of 2000 and 2006 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 2006

List of positive integer factors of 2006 that divides 2006 without a remainder.

1,2,17,34,59,118,1003,2006

Greatest Common Factor

We found the factors and prime factorization of 2000 and 2006. The biggest common factor number is the GCF number.
So the greatest common factor 2000 and 2006 is 2.

Also check out the Least Common Multiple of 2000 and 2006

Properties of GCF 2000 and 2006

(i) The GCF of 2000 and 2006 is associative

GCF of 2000 and 2006 = GCF of 2006 and 2000

Related Greatest Common Factor of 2000

Related Greatest Common Factor of 2006

Frequently Asked Questions on GCF of 2000 and 2006

1. What is the GCF of 2000 and 2006?

Answer: GCF of 2000 and 2006 is 2.

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 2006?

Answer: Factors of 2006 are 1, 2, 17, 34, 59, 118, 1003, 2006. There are 8 integers that are factors of 2006. The greatest factor of 2006 is 2006.

4. How to Find the GCF of 2000 and 2006?

Answer:

Greatest Common Factor of 2000 and 2006 = 2

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 2006

2006 = 2 x 17 x 59

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

GCF = 2

Step 4: Therefore, the greatest common factor of 2000 and 2006 is 2