Greatest Common Factor of 2106 and 2109

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 2106, 2109 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 2106 and 2109 is 3.

GCF(2106,2109) = 3

GCF of 2106 and 2109

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

GCF of:
and

Greatest Common Factor of 2106 and 2109

GCF of 2106 and 2109 is 3

Prime Factorization of 2106


2 2106
3 1053
3 351
3 117
3 39
13 13
1

Prime factors of 2106 are 2,3,13. Prime factorization of 2106 in exponential form is:

2106 = 21×34×131

Prime Factorization of 2109


3 2109
19 703
37 37
1

Prime factors of 2109 are 3,19,37. Prime factorization of 2109 in exponential form is:

2109 = 31×191×371

∴ So by taking common prime factors GCF of 2106 and 2109 is 3

Greatest Common Factor of 2106 and 2109 by matching factors method

Factors of 2106

List of positive integer factors of 2106 that divides 2106 without a remainder.

1,2,3,6,9,13,18,26,27,39,54,78,81,117,162,234,351,702,1053,2106

Factors of 2109

List of positive integer factors of 2109 that divides 2109 without a remainder.

1,3,19,37,57,111,703,2109

Greatest Common Factor

We found the factors and prime factorization of 2106 and 2109. The biggest common factor number is the GCF number.
So the greatest common factor 2106 and 2109 is 3.

Also check out the Least Common Multiple of 2106 and 2109

Properties of GCF 2106 and 2109

(i) The GCF of 2106 and 2109 is associative

GCF of 2106 and 2109 = GCF of 2109 and 2106

Related Greatest Common Factor of 2106

Related Greatest Common Factor of 2109

Frequently Asked Questions on GCF of 2106 and 2109

1. What is the GCF of 2106 and 2109?

Answer: GCF of 2106 and 2109 is 3.

2. What are the Factors of 2106?

Answer: Factors of 2106 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 81, 117, 162, 234, 351, 702, 1053, 2106. There are 20 integers that are factors of 2106. The greatest factor of 2106 is 2106.

3. What are the Factors of 2109?

Answer: Factors of 2109 are 1, 3, 19, 37, 57, 111, 703, 2109. There are 8 integers that are factors of 2109. The greatest factor of 2109 is 2109.

4. How to Find the GCF of 2106 and 2109?

Answer:

Greatest Common Factor of 2106 and 2109 = 3

Step 1: Find the prime factorization of 2106

2106 = 2 x 3 x 3 x 3 x 3 x 13

Step 2: Find the prime factorization of 2109

2109 = 3 x 19 x 37

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

GCF = 3

Step 4: Therefore, the greatest common factor of 2106 and 2109 is 3