Greatest Common Factor of 2198 and 2200

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 2198, 2200 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 2198 and 2200 is 2.

GCF(2198,2200) = 2

GCF of 2198 and 2200

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

GCF of:
and

Greatest Common Factor of 2198 and 2200

GCF of 2198 and 2200 is 2

Prime Factorization of 2198


2 2198
7 1099
157 157
1

Prime factors of 2198 are 2,7,157. Prime factorization of 2198 in exponential form is:

2198 = 21×71×1571

Prime Factorization of 2200


2 2200
2 1100
2 550
5 275
5 55
11 11
1

Prime factors of 2200 are 2,5,11. Prime factorization of 2200 in exponential form is:

2200 = 23×52×111

∴ So by taking common prime factors GCF of 2198 and 2200 is 2

Greatest Common Factor of 2198 and 2200 by matching factors method

Factors of 2198

List of positive integer factors of 2198 that divides 2198 without a remainder.

1,2,7,14,157,314,1099,2198

Factors of 2200

List of positive integer factors of 2200 that divides 2200 without a remainder.

1,2,4,5,8,10,11,20,22,25,40,44,50,55,88,100,110,200,220,275,440,550,1100,2200

Greatest Common Factor

We found the factors and prime factorization of 2198 and 2200. The biggest common factor number is the GCF number.
So the greatest common factor 2198 and 2200 is 2.

Also check out the Least Common Multiple of 2198 and 2200

Properties of GCF 2198 and 2200

(i) The GCF of 2198 and 2200 is associative

GCF of 2198 and 2200 = GCF of 2200 and 2198

Related Greatest Common Factor of 2198

Related Greatest Common Factor of 2200

Frequently Asked Questions on GCF of 2198 and 2200

1. What is the GCF of 2198 and 2200?

Answer: GCF of 2198 and 2200 is 2.

2. What are the Factors of 2198?

Answer: Factors of 2198 are 1, 2, 7, 14, 157, 314, 1099, 2198. There are 8 integers that are factors of 2198. The greatest factor of 2198 is 2198.

3. What are the Factors of 2200?

Answer: Factors of 2200 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 25, 40, 44, 50, 55, 88, 100, 110, 200, 220, 275, 440, 550, 1100, 2200. There are 24 integers that are factors of 2200. The greatest factor of 2200 is 2200.

4. How to Find the GCF of 2198 and 2200?

Answer:

Greatest Common Factor of 2198 and 2200 = 2

Step 1: Find the prime factorization of 2198

2198 = 2 x 7 x 157

Step 2: Find the prime factorization of 2200

2200 = 2 x 2 x 2 x 5 x 5 x 11

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 2198 and 2200 is 2