What are the divisors of 5293?

1, 67, 79, 5293

There is a total of 4 positive divisors.
The sum of these divisors is 5440.
The arithmetic mean is 1360.

4 odd divisors

1, 67, 79, 5293

How to compute the divisors of 5293?

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 5293 by each of the numbers from 1 to 5293 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)

5293 / 1 = 5293 (the remainder is 0, so 1 is a divisor of 5293)
5293 / 2 = 2646.5 (the remainder is 1, so 2 is not a divisor of 5293)
5293 / 3 = 1764.3333333333 (the remainder is 1, so 3 is not a divisor of 5293)
...
5293 / 5292 = 1.0001889644747 (the remainder is 1, so 5292 is not a divisor of 5293)
5293 / 5293 = 1 (the remainder is 0, so 5293 is a divisor of 5293)

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 5293 (i.e. 72.753006810715). 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 $\frac{N}{d} = D$ )

5293 / 1 = 5293 (the remainder is 0, so 1 and 5293 are divisors of 5293)
5293 / 2 = 2646.5 (the remainder is 1, so 2 is not a divisor of 5293)
5293 / 3 = 1764.3333333333 (the remainder is 1, so 3 is not a divisor of 5293)
...
5293 / 71 = 74.549295774648 (the remainder is 39, so 71 is not a divisor of 5293)
5293 / 72 = 73.513888888889 (the remainder is 37, so 72 is not a divisor of 5293)