What are the divisors of 5881?

1, 5881

There is a total of 2 positive divisors.
The sum of these divisors is 5882.
The arithmetic mean is 2941.

2 odd divisors

1, 5881

How to compute the divisors of 5881?

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 5881 by each of the numbers from 1 to 5881 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)

5881 / 1 = 5881 (the remainder is 0, so 1 is a divisor of 5881)
5881 / 2 = 2940.5 (the remainder is 1, so 2 is not a divisor of 5881)
5881 / 3 = 1960.3333333333 (the remainder is 1, so 3 is not a divisor of 5881)
...
5881 / 5880 = 1.0001700680272 (the remainder is 1, so 5880 is not a divisor of 5881)
5881 / 5881 = 1 (the remainder is 0, so 5881 is a divisor of 5881)

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 5881 (i.e. 76.687678280151). 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 $\frac{N}{d} = D$ )

5881 / 1 = 5881 (the remainder is 0, so 1 and 5881 are divisors of 5881)
5881 / 2 = 2940.5 (the remainder is 1, so 2 is not a divisor of 5881)
5881 / 3 = 1960.3333333333 (the remainder is 1, so 3 is not a divisor of 5881)
...
5881 / 75 = 78.413333333333 (the remainder is 31, so 75 is not a divisor of 5881)
5881 / 76 = 77.381578947368 (the remainder is 29, so 76 is not a divisor of 5881)