Greatest Common Factor of 1998 and 2002

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, 2002 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1998 and 2002 is 2.

GCF(1998,2002) = 2

GCF of 1998 and 2002

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 1998 and 2002

GCF of 1998 and 2002 is 2

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 2002


2 2002
7 1001
11 143
13 13
1

Prime factors of 2002 are 2,7,11,13. Prime factorization of 2002 in exponential form is:

2002 = 21×71×111×131

∴ So by taking common prime factors GCF of 1998 and 2002 is 2

Greatest Common Factor of 1998 and 2002 by matching factors method

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 2002

List of positive integer factors of 2002 that divides 2002 without a remainder.

1,2,7,11,13,14,22,26,77,91,143,154,182,286,1001,2002

Greatest Common Factor

We found the factors and prime factorization of 1998 and 2002. The biggest common factor number is the GCF number.
So the greatest common factor 1998 and 2002 is 2.

Also check out the Least Common Multiple of 1998 and 2002

Properties of GCF 1998 and 2002

(i) The GCF of 1998 and 2002 is associative

GCF of 1998 and 2002 = GCF of 2002 and 1998

Related Greatest Common Factor of 1998

Related Greatest Common Factor of 2002

Frequently Asked Questions on GCF of 1998 and 2002

1. What is the GCF of 1998 and 2002?

Answer: GCF of 1998 and 2002 is 2.

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 2002?

Answer: Factors of 2002 are 1, 2, 7, 11, 13, 14, 22, 26, 77, 91, 143, 154, 182, 286, 1001, 2002. There are 16 integers that are factors of 2002. The greatest factor of 2002 is 2002.

4. How to Find the GCF of 1998 and 2002?

Answer:

Greatest Common Factor of 1998 and 2002 = 2

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 2002

2002 = 2 x 7 x 11 x 13

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2

Step 4: Therefore, the greatest common factor of 1998 and 2002 is 2