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 2005, 2007 i.e. 1 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 2005 and 2007 is 1.
GCF(2005,2007) = 1
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
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
Prime Factorization of 2007
3 | 2007 |
3 | 669 |
223 | 223 |
1 |
Prime factors of 2007 are 3,223. Prime factorization of 2007 in exponential form is:
2007 = 32×2231
∴ So by taking common prime factors GCF of 2005 and 2007 is 1
Factors of 2005
List of positive integer factors of 2005 that divides 2005 without a remainder.
1,5,401,2005
Factors of 2007
List of positive integer factors of 2007 that divides 2007 without a remainder.
1,3,9,223,669,2007
Greatest Common Factor
We found the factors and prime factorization of 2005 and 2007. The biggest common factor number is the GCF number.
So the greatest common factor 2005 and 2007 is 1.
Also check out the Least Common Multiple of 2005 and 2007
(i) The GCF of 2005 and 2007 is associative
GCF of 2005 and 2007 = GCF of 2007 and 2005
1. What is the GCF of 2005 and 2007?
Answer: GCF of 2005 and 2007 is 1.
2. 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.
3. What are the Factors of 2007?
Answer: Factors of 2007 are 1, 3, 9, 223, 669, 2007. There are 6 integers that are factors of 2007. The greatest factor of 2007 is 2007.
4. How to Find the GCF of 2005 and 2007?
Answer:
Greatest Common Factor of 2005 and 2007 = 1
Step 1: Find the prime factorization of 2005
2005 = 5 x 401
Step 2: Find the prime factorization of 2007
2007 = 3 x 3 x 223
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = = 1
Step 4: Therefore, the greatest common factor of 2005 and 2007 is 1