What are the divisors of 5539?

1, 29, 191, 5539

There is a total of 4 positive divisors.
The sum of these divisors is 5760.
The arithmetic mean is 1440.

4 odd divisors

1, 29, 191, 5539

How to compute the divisors of 5539?

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 5539 by each of the numbers from 1 to 5539 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)

5539 / 1 = 5539 (the remainder is 0, so 1 is a divisor of 5539)
5539 / 2 = 2769.5 (the remainder is 1, so 2 is not a divisor of 5539)
5539 / 3 = 1846.3333333333 (the remainder is 1, so 3 is not a divisor of 5539)
...
5539 / 5538 = 1.0001805706031 (the remainder is 1, so 5538 is not a divisor of 5539)
5539 / 5539 = 1 (the remainder is 0, so 5539 is a divisor of 5539)

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 5539 (i.e. 74.424458345358). 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 $\frac{N}{d} = D$ )

5539 / 1 = 5539 (the remainder is 0, so 1 and 5539 are divisors of 5539)
5539 / 2 = 2769.5 (the remainder is 1, so 2 is not a divisor of 5539)
5539 / 3 = 1846.3333333333 (the remainder is 1, so 3 is not a divisor of 5539)
...
5539 / 73 = 75.876712328767 (the remainder is 64, so 73 is not a divisor of 5539)
5539 / 74 = 74.851351351351 (the remainder is 63, so 74 is not a divisor of 5539)