Greatest Common Factor of 2000 and 2002

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, 2002 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 2000 and 2002 is 2.

GCF(2000,2002) = 2

GCF of 2000 and 2002

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

GCF of:
and

Greatest Common Factor of 2000 and 2002

GCF of 2000 and 2002 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 2002


2 2002
7 1001
11 143
13 13
1

Prime factors of 2002 are 2,7,11,13. Prime factorization of 2002 in exponential form is:

2002 = 21×71×111×131

∴ So by taking common prime factors GCF of 2000 and 2002 is 2

Greatest Common Factor of 2000 and 2002 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 2002

List of positive integer factors of 2002 that divides 2002 without a remainder.

1,2,7,11,13,14,22,26,77,91,143,154,182,286,1001,2002

Greatest Common Factor

We found the factors and prime factorization of 2000 and 2002. The biggest common factor number is the GCF number.
So the greatest common factor 2000 and 2002 is 2.

Also check out the Least Common Multiple of 2000 and 2002

Properties of GCF 2000 and 2002

(i) The GCF of 2000 and 2002 is associative

GCF of 2000 and 2002 = GCF of 2002 and 2000

Related Greatest Common Factor of 2000

Related Greatest Common Factor of 2002

Frequently Asked Questions on GCF of 2000 and 2002

1. What is the GCF of 2000 and 2002?

Answer: GCF of 2000 and 2002 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 2002?

Answer: Factors of 2002 are 1, 2, 7, 11, 13, 14, 22, 26, 77, 91, 143, 154, 182, 286, 1001, 2002. There are 16 integers that are factors of 2002. The greatest factor of 2002 is 2002.

4. How to Find the GCF of 2000 and 2002?

Answer:

Greatest Common Factor of 2000 and 2002 = 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 2002

2002 = 2 x 7 x 11 x 13

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 2002 is 2