Greatest Common Factor of 2109 and 2112

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 2109, 2112 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 2109 and 2112 is 3.

GCF(2109,2112) = 3

GCF of 2109 and 2112

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

GCF of:
and

Greatest Common Factor of 2109 and 2112

GCF of 2109 and 2112 is 3

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

Prime Factorization of 2112


2 2112
2 1056
2 528
2 264
2 132
2 66
3 33
11 11
1

Prime factors of 2112 are 2,3,11. Prime factorization of 2112 in exponential form is:

2112 = 26×31×111

∴ So by taking common prime factors GCF of 2109 and 2112 is 3

Greatest Common Factor of 2109 and 2112 by matching factors method

Factors of 2109

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

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

Factors of 2112

List of positive integer factors of 2112 that divides 2112 without a remainder.

1,2,3,4,6,8,11,12,16,22,24,32,33,44,48,64,66,88,96,132,176,192,264,352,528,704,1056,2112

Greatest Common Factor

We found the factors and prime factorization of 2109 and 2112. The biggest common factor number is the GCF number.
So the greatest common factor 2109 and 2112 is 3.

Also check out the Least Common Multiple of 2109 and 2112

Properties of GCF 2109 and 2112

(i) The GCF of 2109 and 2112 is associative

GCF of 2109 and 2112 = GCF of 2112 and 2109

Related Greatest Common Factor of 2109

Related Greatest Common Factor of 2112

Frequently Asked Questions on GCF of 2109 and 2112

1. What is the GCF of 2109 and 2112?

Answer: GCF of 2109 and 2112 is 3.

2. 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.

3. What are the Factors of 2112?

Answer: Factors of 2112 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 64, 66, 88, 96, 132, 176, 192, 264, 352, 528, 704, 1056, 2112. There are 28 integers that are factors of 2112. The greatest factor of 2112 is 2112.

4. How to Find the GCF of 2109 and 2112?

Answer:

Greatest Common Factor of 2109 and 2112 = 3

Step 1: Find the prime factorization of 2109

2109 = 3 x 19 x 37

Step 2: Find the prime factorization of 2112

2112 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 11

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 2109 and 2112 is 3