What are the divisors of 2341?
1, 2341
- There is a total of 2 positive divisors.
- The sum of these divisors is 2342.
- The arithmetic mean is 1171.
2 odd divisors
1, 2341
How to compute the divisors of 2341?
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 2341 by each of the numbers from 1 to 2341 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 2341 / 1 = 2341 (the remainder is 0, so 1 is a divisor of 2341)
- 2341 / 2 = 1170.5 (the remainder is 1, so 2 is not a divisor of 2341)
- 2341 / 3 = 780.33333333333 (the remainder is 1, so 3 is not a divisor of 2341)
- ...
- 2341 / 2340 = 1.0004273504274 (the remainder is 1, so 2340 is not a divisor of 2341)
- 2341 / 2341 = 1 (the remainder is 0, so 2341 is a divisor of 2341)
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 2341 (i.e. 48.383881613612). 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 )
- 2341 / 1 = 2341 (the remainder is 0, so 1 and 2341 are divisors of 2341)
- 2341 / 2 = 1170.5 (the remainder is 1, so 2 is not a divisor of 2341)
- 2341 / 3 = 780.33333333333 (the remainder is 1, so 3 is not a divisor of 2341)
- ...
- 2341 / 47 = 49.808510638298 (the remainder is 38, so 47 is not a divisor of 2341)
- 2341 / 48 = 48.770833333333 (the remainder is 37, so 48 is not a divisor of 2341)