Greatest Common Factor of 2200 and 2208

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 2200, 2208 i.e. 8 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 2200 and 2208 is 8.

GCF(2200,2208) = 8

GCF of 2200 and 2208

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

GCF of:
and

Greatest Common Factor of 2200 and 2208

GCF of 2200 and 2208 is 8

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

Prime Factorization of 2208


2 2208
2 1104
2 552
2 276
2 138
3 69
23 23
1

Prime factors of 2208 are 2,3,23. Prime factorization of 2208 in exponential form is:

2208 = 25×31×231

∴ So by taking common prime factors GCF of 2200 and 2208 is 8

Greatest Common Factor of 2200 and 2208 by matching factors method

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

Factors of 2208

List of positive integer factors of 2208 that divides 2208 without a remainder.

1,2,3,4,6,8,12,16,23,24,32,46,48,69,92,96,138,184,276,368,552,736,1104,2208

Greatest Common Factor

We found the factors and prime factorization of 2200 and 2208. The biggest common factor number is the GCF number.
So the greatest common factor 2200 and 2208 is 8.

Also check out the Least Common Multiple of 2200 and 2208

Properties of GCF 2200 and 2208

(i) The GCF of 2200 and 2208 is associative

GCF of 2200 and 2208 = GCF of 2208 and 2200

Related Greatest Common Factor of 2200

Related Greatest Common Factor of 2208

Frequently Asked Questions on GCF of 2200 and 2208

1. What is the GCF of 2200 and 2208?

Answer: GCF of 2200 and 2208 is 8.

2. 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.

3. What are the Factors of 2208?

Answer: Factors of 2208 are 1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 32, 46, 48, 69, 92, 96, 138, 184, 276, 368, 552, 736, 1104, 2208. There are 24 integers that are factors of 2208. The greatest factor of 2208 is 2208.

4. How to Find the GCF of 2200 and 2208?

Answer:

Greatest Common Factor of 2200 and 2208 = 8

Step 1: Find the prime factorization of 2200

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

Step 2: Find the prime factorization of 2208

2208 = 2 x 2 x 2 x 2 x 2 x 3 x 23

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

GCF = 2 x 2 x 2 = 8

Step 4: Therefore, the greatest common factor of 2200 and 2208 is 8