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 1998, 2005 i.e. 1 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 1998 and 2005 is 1.
GCF(1998,2005) = 1
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 1998
2 | 1998 |
3 | 999 |
3 | 333 |
3 | 111 |
37 | 37 |
1 |
Prime factors of 1998 are 2,3,37. Prime factorization of 1998 in exponential form is:
1998 = 21×33×371
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
∴ So by taking common prime factors GCF of 1998 and 2005 is 1
Factors of 1998
List of positive integer factors of 1998 that divides 1998 without a remainder.
1,2,3,6,9,18,27,37,54,74,111,222,333,666,999,1998
Factors of 2005
List of positive integer factors of 2005 that divides 2005 without a remainder.
1,5,401,2005
Greatest Common Factor
We found the factors and prime factorization of 1998 and 2005. The biggest common factor number is the GCF number.
So the greatest common factor 1998 and 2005 is 1.
Also check out the Least Common Multiple of 1998 and 2005
(i) The GCF of 1998 and 2005 is associative
GCF of 1998 and 2005 = GCF of 2005 and 1998
1. What is the GCF of 1998 and 2005?
Answer: GCF of 1998 and 2005 is 1.
2. What are the Factors of 1998?
Answer: Factors of 1998 are 1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 111, 222, 333, 666, 999, 1998. There are 16 integers that are factors of 1998. The greatest factor of 1998 is 1998.
3. 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.
4. How to Find the GCF of 1998 and 2005?
Answer:
Greatest Common Factor of 1998 and 2005 = 1
Step 1: Find the prime factorization of 1998
1998 = 2 x 3 x 3 x 3 x 37
Step 2: Find the prime factorization of 2005
2005 = 5 x 401
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 1998 and 2005 is 1