What are the divisors of 5882?

1, 2, 17, 34, 173, 346, 2941, 5882

There is a total of 8 positive divisors.
The sum of these divisors is 9396.
The arithmetic mean is 1174.5.

4 even divisors

2, 34, 346, 5882

4 odd divisors

1, 17, 173, 2941

How to compute the divisors of 5882?

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 5882 by each of the numbers from 1 to 5882 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)

5882 / 1 = 5882 (the remainder is 0, so 1 is a divisor of 5882)
5882 / 2 = 2941 (the remainder is 0, so 2 is a divisor of 5882)
5882 / 3 = 1960.6666666667 (the remainder is 2, so 3 is not a divisor of 5882)
...
5882 / 5881 = 1.000170039109 (the remainder is 1, so 5881 is not a divisor of 5882)
5882 / 5882 = 1 (the remainder is 0, so 5882 is a divisor of 5882)

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 5882 (i.e. 76.694197955256). 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 $\frac{N}{d} = D$ )

5882 / 1 = 5882 (the remainder is 0, so 1 and 5882 are divisors of 5882)
5882 / 2 = 2941 (the remainder is 0, so 2 and 2941 are divisors of 5882)
5882 / 3 = 1960.6666666667 (the remainder is 2, so 3 is not a divisor of 5882)
...
5882 / 75 = 78.426666666667 (the remainder is 32, so 75 is not a divisor of 5882)
5882 / 76 = 77.394736842105 (the remainder is 30, so 76 is not a divisor of 5882)