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 2103, 2106 i.e. 3 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 2103 and 2106 is 3.
GCF(2103,2106) = 3
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 2103
3 | 2103 |
701 | 701 |
1 |
Prime factors of 2103 are 3,701. Prime factorization of 2103 in exponential form is:
2103 = 31×7011
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
∴ So by taking common prime factors GCF of 2103 and 2106 is 3
Factors of 2103
List of positive integer factors of 2103 that divides 2103 without a remainder.
1,3,701,2103
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
Greatest Common Factor
We found the factors and prime factorization of 2103 and 2106. The biggest common factor number is the GCF number.
So the greatest common factor 2103 and 2106 is 3.
Also check out the Least Common Multiple of 2103 and 2106
(i) The GCF of 2103 and 2106 is associative
GCF of 2103 and 2106 = GCF of 2106 and 2103
1. What is the GCF of 2103 and 2106?
Answer: GCF of 2103 and 2106 is 3.
2. What are the Factors of 2103?
Answer: Factors of 2103 are 1, 3, 701, 2103. There are 4 integers that are factors of 2103. The greatest factor of 2103 is 2103.
3. 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.
4. How to Find the GCF of 2103 and 2106?
Answer:
Greatest Common Factor of 2103 and 2106 = 3
Step 1: Find the prime factorization of 2103
2103 = 3 x 701
Step 2: Find the prime factorization of 2106
2106 = 2 x 3 x 3 x 3 x 3 x 13
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 2103 and 2106 is 3