What are the divisors of 2543?

1, 2543

There is a total of 2 positive divisors.
The sum of these divisors is 2544.
The arithmetic mean is 1272.

2 odd divisors

1, 2543

How to compute the divisors of 2543?

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.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 2543 by each of the numbers from 1 to 2543 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

2543 / 1 = 2543 (the remainder is 0, so 1 is a divisor of 2543)
2543 / 2 = 1271.5 (the remainder is 1, so 2 is not a divisor of 2543)
2543 / 3 = 847.66666666667 (the remainder is 2, so 3 is not a divisor of 2543)
...
2543 / 2542 = 1.0003933910307 (the remainder is 1, so 2542 is not a divisor of 2543)
2543 / 2543 = 1 (the remainder is 0, so 2543 is a divisor of 2543)

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 2543 (i.e. 50.428166732492). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

2543 / 1 = 2543 (the remainder is 0, so 1 and 2543 are divisors of 2543)
2543 / 2 = 1271.5 (the remainder is 1, so 2 is not a divisor of 2543)
2543 / 3 = 847.66666666667 (the remainder is 2, so 3 is not a divisor of 2543)
...
2543 / 49 = 51.897959183673 (the remainder is 44, so 49 is not a divisor of 2543)
2543 / 50 = 50.86 (the remainder is 43, so 50 is not a divisor of 2543)