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, 2004 i.e. 6 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 1998 and 2004 is 6.
GCF(1998,2004) = 6
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 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
∴ So by taking common prime factors GCF of 1998 and 2004 is 6
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 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
Greatest Common Factor
We found the factors and prime factorization of 1998 and 2004. The biggest common factor number is the GCF number.
So the greatest common factor 1998 and 2004 is 6.
Also check out the Least Common Multiple of 1998 and 2004
(i) The GCF of 1998 and 2004 is associative
GCF of 1998 and 2004 = GCF of 2004 and 1998
1. What is the GCF of 1998 and 2004?
Answer: GCF of 1998 and 2004 is 6.
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 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.
4. How to Find the GCF of 1998 and 2004?
Answer:
Greatest Common Factor of 1998 and 2004 = 6
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 2004
2004 = 2 x 2 x 3 x 167
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = 2 x 3 = 6
Step 4: Therefore, the greatest common factor of 1998 and 2004 is 6