What are the divisors of 5093?

1, 11, 463, 5093

There is a total of 4 positive divisors.
The sum of these divisors is 5568.
The arithmetic mean is 1392.

4 odd divisors

1, 11, 463, 5093

How to compute the divisors of 5093?

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 5093 by each of the numbers from 1 to 5093 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)

5093 / 1 = 5093 (the remainder is 0, so 1 is a divisor of 5093)
5093 / 2 = 2546.5 (the remainder is 1, so 2 is not a divisor of 5093)
5093 / 3 = 1697.6666666667 (the remainder is 2, so 3 is not a divisor of 5093)
...
5093 / 5092 = 1.0001963864886 (the remainder is 1, so 5092 is not a divisor of 5093)
5093 / 5093 = 1 (the remainder is 0, so 5093 is a divisor of 5093)

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 5093 (i.e. 71.365257653847). 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 $\frac{N}{d} = D$ )

5093 / 1 = 5093 (the remainder is 0, so 1 and 5093 are divisors of 5093)
5093 / 2 = 2546.5 (the remainder is 1, so 2 is not a divisor of 5093)
5093 / 3 = 1697.6666666667 (the remainder is 2, so 3 is not a divisor of 5093)
...
5093 / 70 = 72.757142857143 (the remainder is 53, so 70 is not a divisor of 5093)
5093 / 71 = 71.732394366197 (the remainder is 52, so 71 is not a divisor of 5093)