What are the divisors of 5941?

1, 13, 457, 5941

There is a total of 4 positive divisors.
The sum of these divisors is 6412.
The arithmetic mean is 1603.

4 odd divisors

1, 13, 457, 5941

How to compute the divisors of 5941?

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 5941 by each of the numbers from 1 to 5941 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)

5941 / 1 = 5941 (the remainder is 0, so 1 is a divisor of 5941)
5941 / 2 = 2970.5 (the remainder is 1, so 2 is not a divisor of 5941)
5941 / 3 = 1980.3333333333 (the remainder is 1, so 3 is not a divisor of 5941)
...
5941 / 5940 = 1.0001683501684 (the remainder is 1, so 5940 is not a divisor of 5941)
5941 / 5941 = 1 (the remainder is 0, so 5941 is a divisor of 5941)

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 5941 (i.e. 77.077882690173). 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 $\frac{N}{d} = D$ )

5941 / 1 = 5941 (the remainder is 0, so 1 and 5941 are divisors of 5941)
5941 / 2 = 2970.5 (the remainder is 1, so 2 is not a divisor of 5941)
5941 / 3 = 1980.3333333333 (the remainder is 1, so 3 is not a divisor of 5941)
...
5941 / 76 = 78.171052631579 (the remainder is 13, so 76 is not a divisor of 5941)
5941 / 77 = 77.155844155844 (the remainder is 12, so 77 is not a divisor of 5941)