What are the divisors of 5183?

1, 71, 73, 5183

There is a total of 4 positive divisors.
The sum of these divisors is 5328.
The arithmetic mean is 1332.

4 odd divisors

1, 71, 73, 5183

How to compute the divisors of 5183?

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 5183 by each of the numbers from 1 to 5183 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)

5183 / 1 = 5183 (the remainder is 0, so 1 is a divisor of 5183)
5183 / 2 = 2591.5 (the remainder is 1, so 2 is not a divisor of 5183)
5183 / 3 = 1727.6666666667 (the remainder is 2, so 3 is not a divisor of 5183)
...
5183 / 5182 = 1.0001929756851 (the remainder is 1, so 5182 is not a divisor of 5183)
5183 / 5183 = 1 (the remainder is 0, so 5183 is a divisor of 5183)

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 5183 (i.e. 71.993055220625). 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 $\frac{N}{d} = D$ )

5183 / 1 = 5183 (the remainder is 0, so 1 and 5183 are divisors of 5183)
5183 / 2 = 2591.5 (the remainder is 1, so 2 is not a divisor of 5183)
5183 / 3 = 1727.6666666667 (the remainder is 2, so 3 is not a divisor of 5183)
...
5183 / 70 = 74.042857142857 (the remainder is 3, so 70 is not a divisor of 5183)
5183 / 71 = 73 (the remainder is 0, so 71 and 73 are divisors of 5183)