What are the divisors of 5359?

1, 23, 233, 5359

There is a total of 4 positive divisors.
The sum of these divisors is 5616.
The arithmetic mean is 1404.

4 odd divisors

1, 23, 233, 5359

How to compute the divisors of 5359?

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 5359 by each of the numbers from 1 to 5359 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)

5359 / 1 = 5359 (the remainder is 0, so 1 is a divisor of 5359)
5359 / 2 = 2679.5 (the remainder is 1, so 2 is not a divisor of 5359)
5359 / 3 = 1786.3333333333 (the remainder is 1, so 3 is not a divisor of 5359)
...
5359 / 5358 = 1.0001866368048 (the remainder is 1, so 5358 is not a divisor of 5359)
5359 / 5359 = 1 (the remainder is 0, so 5359 is a divisor of 5359)

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 5359 (i.e. 73.205191072765). 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 $\frac{N}{d} = D$ )

5359 / 1 = 5359 (the remainder is 0, so 1 and 5359 are divisors of 5359)
5359 / 2 = 2679.5 (the remainder is 1, so 2 is not a divisor of 5359)
5359 / 3 = 1786.3333333333 (the remainder is 1, so 3 is not a divisor of 5359)
...
5359 / 72 = 74.430555555556 (the remainder is 31, so 72 is not a divisor of 5359)
5359 / 73 = 73.41095890411 (the remainder is 30, so 73 is not a divisor of 5359)