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
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
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
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
(i) The GCF of 2109 and 2112 is associative
GCF of 2109 and 2112 = GCF of 2112 and 2109
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