What are the divisors of 5541?

1, 3, 1847, 5541

There is a total of 4 positive divisors.
The sum of these divisors is 7392.
The arithmetic mean is 1848.

4 odd divisors

1, 3, 1847, 5541

How to compute the divisors of 5541?

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 5541 by each of the numbers from 1 to 5541 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)

5541 / 1 = 5541 (the remainder is 0, so 1 is a divisor of 5541)
5541 / 2 = 2770.5 (the remainder is 1, so 2 is not a divisor of 5541)
5541 / 3 = 1847 (the remainder is 0, so 3 is a divisor of 5541)
...
5541 / 5540 = 1.0001805054152 (the remainder is 1, so 5540 is not a divisor of 5541)
5541 / 5541 = 1 (the remainder is 0, so 5541 is a divisor of 5541)

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 5541 (i.e. 74.437893575786). 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 $\frac{N}{d} = D$ )

5541 / 1 = 5541 (the remainder is 0, so 1 and 5541 are divisors of 5541)
5541 / 2 = 2770.5 (the remainder is 1, so 2 is not a divisor of 5541)
5541 / 3 = 1847 (the remainder is 0, so 3 and 1847 are divisors of 5541)
...
5541 / 73 = 75.904109589041 (the remainder is 66, so 73 is not a divisor of 5541)
5541 / 74 = 74.878378378378 (the remainder is 65, so 74 is not a divisor of 5541)