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 2108, 2112 i.e. 4 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 2108 and 2112 is 4.
GCF(2108,2112) = 4
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 2108
2 | 2108 |
2 | 1054 |
17 | 527 |
31 | 31 |
1 |
Prime factors of 2108 are 2,17,31. Prime factorization of 2108 in exponential form is:
2108 = 22×171×311
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 2108 and 2112 is 4
Factors of 2108
List of positive integer factors of 2108 that divides 2108 without a remainder.
1,2,4,17,31,34,62,68,124,527,1054,2108
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 2108 and 2112. The biggest common factor number is the GCF number.
So the greatest common factor 2108 and 2112 is 4.
Also check out the Least Common Multiple of 2108 and 2112
(i) The GCF of 2108 and 2112 is associative
GCF of 2108 and 2112 = GCF of 2112 and 2108
1. What is the GCF of 2108 and 2112?
Answer: GCF of 2108 and 2112 is 4.
2. What are the Factors of 2108?
Answer: Factors of 2108 are 1, 2, 4, 17, 31, 34, 62, 68, 124, 527, 1054, 2108. There are 12 integers that are factors of 2108. The greatest factor of 2108 is 2108.
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 2108 and 2112?
Answer:
Greatest Common Factor of 2108 and 2112 = 4
Step 1: Find the prime factorization of 2108
2108 = 2 x 2 x 17 x 31
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 = 2 x 2 = 4
Step 4: Therefore, the greatest common factor of 2108 and 2112 is 4