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 2004, 2008 i.e. 4 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 2004 and 2008 is 4.
GCF(2004,2008) = 4
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 2004
2 | 2004 |
2 | 1002 |
3 | 501 |
167 | 167 |
1 |
Prime factors of 2004 are 2,3,167. Prime factorization of 2004 in exponential form is:
2004 = 22×31×1671
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 2004 and 2008 is 4
Factors of 2004
List of positive integer factors of 2004 that divides 2004 without a remainder.
1,2,3,4,6,12,167,334,501,668,1002,2004
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 2004 and 2008. The biggest common factor number is the GCF number.
So the greatest common factor 2004 and 2008 is 4.
Also check out the Least Common Multiple of 2004 and 2008
(i) The GCF of 2004 and 2008 is associative
GCF of 2004 and 2008 = GCF of 2008 and 2004
1. What is the GCF of 2004 and 2008?
Answer: GCF of 2004 and 2008 is 4.
2. What are the Factors of 2004?
Answer: Factors of 2004 are 1, 2, 3, 4, 6, 12, 167, 334, 501, 668, 1002, 2004. There are 12 integers that are factors of 2004. The greatest factor of 2004 is 2004.
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 2004 and 2008?
Answer:
Greatest Common Factor of 2004 and 2008 = 4
Step 1: Find the prime factorization of 2004
2004 = 2 x 2 x 3 x 167
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 x 2 = 4
Step 4: Therefore, the greatest common factor of 2004 and 2008 is 4