What are the divisors of 5043?

1, 3, 41, 123, 1681, 5043

There is a total of 6 positive divisors.
The sum of these divisors is 6892.
The arithmetic mean is 1148.6666666667.

6 odd divisors

1, 3, 41, 123, 1681, 5043

How to compute the divisors of 5043?

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 5043 by each of the numbers from 1 to 5043 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)

5043 / 1 = 5043 (the remainder is 0, so 1 is a divisor of 5043)
5043 / 2 = 2521.5 (the remainder is 1, so 2 is not a divisor of 5043)
5043 / 3 = 1681 (the remainder is 0, so 3 is a divisor of 5043)
...
5043 / 5042 = 1.0001983339944 (the remainder is 1, so 5042 is not a divisor of 5043)
5043 / 5043 = 1 (the remainder is 0, so 5043 is a divisor of 5043)

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 5043 (i.e. 71.014083110324). 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 $\frac{N}{d} = D$ )

5043 / 1 = 5043 (the remainder is 0, so 1 and 5043 are divisors of 5043)
5043 / 2 = 2521.5 (the remainder is 1, so 2 is not a divisor of 5043)
5043 / 3 = 1681 (the remainder is 0, so 3 and 1681 are divisors of 5043)
...
5043 / 70 = 72.042857142857 (the remainder is 3, so 70 is not a divisor of 5043)
5043 / 71 = 71.028169014085 (the remainder is 2, so 71 is not a divisor of 5043)