What are the divisors of 5339?

1, 19, 281, 5339

There is a total of 4 positive divisors.
The sum of these divisors is 5640.
The arithmetic mean is 1410.

4 odd divisors

1, 19, 281, 5339

How to compute the divisors of 5339?

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 5339 by each of the numbers from 1 to 5339 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)

5339 / 1 = 5339 (the remainder is 0, so 1 is a divisor of 5339)
5339 / 2 = 2669.5 (the remainder is 1, so 2 is not a divisor of 5339)
5339 / 3 = 1779.6666666667 (the remainder is 2, so 3 is not a divisor of 5339)
...
5339 / 5338 = 1.0001873360809 (the remainder is 1, so 5338 is not a divisor of 5339)
5339 / 5339 = 1 (the remainder is 0, so 5339 is a divisor of 5339)

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 5339 (i.e. 73.068461048526). 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 $\frac{N}{d} = D$ )

5339 / 1 = 5339 (the remainder is 0, so 1 and 5339 are divisors of 5339)
5339 / 2 = 2669.5 (the remainder is 1, so 2 is not a divisor of 5339)
5339 / 3 = 1779.6666666667 (the remainder is 2, so 3 is not a divisor of 5339)
...
5339 / 72 = 74.152777777778 (the remainder is 11, so 72 is not a divisor of 5339)
5339 / 73 = 73.13698630137 (the remainder is 10, so 73 is not a divisor of 5339)