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 2009, 2010 i.e. 1 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 2009 and 2010 is 1.
GCF(2009,2010) = 1
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 2009
7 | 2009 |
7 | 287 |
41 | 41 |
1 |
Prime factors of 2009 are 7,41. Prime factorization of 2009 in exponential form is:
2009 = 72×411
Prime Factorization of 2010
2 | 2010 |
3 | 1005 |
5 | 335 |
67 | 67 |
1 |
Prime factors of 2010 are 2,3,5,67. Prime factorization of 2010 in exponential form is:
2010 = 21×31×51×671
∴ So by taking common prime factors GCF of 2009 and 2010 is 1
Factors of 2009
List of positive integer factors of 2009 that divides 2009 without a remainder.
1,7,41,49,287,2009
Factors of 2010
List of positive integer factors of 2010 that divides 2010 without a remainder.
1,2,3,5,6,10,15,30,67,134,201,335,402,670,1005,2010
Greatest Common Factor
We found the factors and prime factorization of 2009 and 2010. The biggest common factor number is the GCF number.
So the greatest common factor 2009 and 2010 is 1.
Also check out the Least Common Multiple of 2009 and 2010
(i) The GCF of 2009 and 2010 is associative
GCF of 2009 and 2010 = GCF of 2010 and 2009
1. What is the GCF of 2009 and 2010?
Answer: GCF of 2009 and 2010 is 1.
2. What are the Factors of 2009?
Answer: Factors of 2009 are 1, 7, 41, 49, 287, 2009. There are 6 integers that are factors of 2009. The greatest factor of 2009 is 2009.
3. What are the Factors of 2010?
Answer: Factors of 2010 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010. There are 16 integers that are factors of 2010. The greatest factor of 2010 is 2010.
4. How to Find the GCF of 2009 and 2010?
Answer:
Greatest Common Factor of 2009 and 2010 = 1
Step 1: Find the prime factorization of 2009
2009 = 7 x 7 x 41
Step 2: Find the prime factorization of 2010
2010 = 2 x 3 x 5 x 67
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 2009 and 2010 is 1