What are the divisors of 2103?
1, 3, 701, 2103
- There is a total of 4 positive divisors.
- The sum of these divisors is 2808.
- The arithmetic mean is 702.
4 odd divisors
1, 3, 701, 2103
How to compute the divisors of 2103?
A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.
Brute force algorithm
We could start by using a brute-force method which would involve dividing 2103 by each of the numbers from 1 to 2103 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 2103 / 1 = 2103 (the remainder is 0, so 1 is a divisor of 2103)
- 2103 / 2 = 1051.5 (the remainder is 1, so 2 is not a divisor of 2103)
- 2103 / 3 = 701 (the remainder is 0, so 3 is a divisor of 2103)
- ...
- 2103 / 2102 = 1.000475737393 (the remainder is 1, so 2102 is not a divisor of 2103)
- 2103 / 2103 = 1 (the remainder is 0, so 2103 is a divisor of 2103)
Improved algorithm using square-root
However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 2103 (i.e. 45.858477951192). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:
(thus, if , then )
- 2103 / 1 = 2103 (the remainder is 0, so 1 and 2103 are divisors of 2103)
- 2103 / 2 = 1051.5 (the remainder is 1, so 2 is not a divisor of 2103)
- 2103 / 3 = 701 (the remainder is 0, so 3 and 701 are divisors of 2103)
- ...
- 2103 / 44 = 47.795454545455 (the remainder is 35, so 44 is not a divisor of 2103)
- 2103 / 45 = 46.733333333333 (the remainder is 33, so 45 is not a divisor of 2103)