Greatest Common Factor of 2002 and 2008

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 2002, 2008 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 2002 and 2008 is 2.

GCF(2002,2008) = 2

GCF of 2002 and 2008

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

GCF of:
and

Greatest Common Factor of 2002 and 2008

GCF of 2002 and 2008 is 2

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

Prime Factorization of 2008


2 2008
2 1004
2 502
251 251
1

Prime factors of 2008 are 2,251. Prime factorization of 2008 in exponential form is:

2008 = 23×2511

∴ So by taking common prime factors GCF of 2002 and 2008 is 2

Greatest Common Factor of 2002 and 2008 by matching factors method

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

Factors of 2008

List of positive integer factors of 2008 that divides 2008 without a remainder.

1,2,4,8,251,502,1004,2008

Greatest Common Factor

We found the factors and prime factorization of 2002 and 2008. The biggest common factor number is the GCF number.
So the greatest common factor 2002 and 2008 is 2.

Also check out the Least Common Multiple of 2002 and 2008

Properties of GCF 2002 and 2008

(i) The GCF of 2002 and 2008 is associative

GCF of 2002 and 2008 = GCF of 2008 and 2002

Related Greatest Common Factor of 2002

Related Greatest Common Factor of 2008

Frequently Asked Questions on GCF of 2002 and 2008

1. What is the GCF of 2002 and 2008?

Answer: GCF of 2002 and 2008 is 2.

2. 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.

3. What are the Factors of 2008?

Answer: Factors of 2008 are 1, 2, 4, 8, 251, 502, 1004, 2008. There are 8 integers that are factors of 2008. The greatest factor of 2008 is 2008.

4. How to Find the GCF of 2002 and 2008?

Answer:

Greatest Common Factor of 2002 and 2008 = 2

Step 1: Find the prime factorization of 2002

2002 = 2 x 7 x 11 x 13

Step 2: Find the prime factorization of 2008

2008 = 2 x 2 x 2 x 251

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 2002 and 2008 is 2