Greatest Common Factor of 2208 and 2214

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 2208, 2214 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 2208 and 2214 is 6.

GCF(2208,2214) = 6

GCF of 2208 and 2214

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

GCF of:
and

Greatest Common Factor of 2208 and 2214

GCF of 2208 and 2214 is 6

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

Prime Factorization of 2214


2 2214
3 1107
3 369
3 123
41 41
1

Prime factors of 2214 are 2,3,41. Prime factorization of 2214 in exponential form is:

2214 = 21×33×411

∴ So by taking common prime factors GCF of 2208 and 2214 is 6

Greatest Common Factor of 2208 and 2214 by matching factors method

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

Factors of 2214

List of positive integer factors of 2214 that divides 2214 without a remainder.

1,2,3,6,9,18,27,41,54,82,123,246,369,738,1107,2214

Greatest Common Factor

We found the factors and prime factorization of 2208 and 2214. The biggest common factor number is the GCF number.
So the greatest common factor 2208 and 2214 is 6.

Also check out the Least Common Multiple of 2208 and 2214

Properties of GCF 2208 and 2214

(i) The GCF of 2208 and 2214 is associative

GCF of 2208 and 2214 = GCF of 2214 and 2208

Related Greatest Common Factor of 2208

Related Greatest Common Factor of 2214

Frequently Asked Questions on GCF of 2208 and 2214

1. What is the GCF of 2208 and 2214?

Answer: GCF of 2208 and 2214 is 6.

2. 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.

3. What are the Factors of 2214?

Answer: Factors of 2214 are 1, 2, 3, 6, 9, 18, 27, 41, 54, 82, 123, 246, 369, 738, 1107, 2214. There are 16 integers that are factors of 2214. The greatest factor of 2214 is 2214.

4. How to Find the GCF of 2208 and 2214?

Answer:

Greatest Common Factor of 2208 and 2214 = 6

Step 1: Find the prime factorization of 2208

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

Step 2: Find the prime factorization of 2214

2214 = 2 x 3 x 3 x 3 x 41

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 2208 and 2214 is 6