What are the divisors of 5831?

1, 7, 17, 49, 119, 343, 833, 5831

There is a total of 8 positive divisors.
The sum of these divisors is 7200.
The arithmetic mean is 900.

8 odd divisors

1, 7, 17, 49, 119, 343, 833, 5831

How to compute the divisors of 5831?

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 5831 by each of the numbers from 1 to 5831 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)

5831 / 1 = 5831 (the remainder is 0, so 1 is a divisor of 5831)
5831 / 2 = 2915.5 (the remainder is 1, so 2 is not a divisor of 5831)
5831 / 3 = 1943.6666666667 (the remainder is 2, so 3 is not a divisor of 5831)
...
5831 / 5830 = 1.0001715265866 (the remainder is 1, so 5830 is not a divisor of 5831)
5831 / 5831 = 1 (the remainder is 0, so 5831 is a divisor of 5831)

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 5831 (i.e. 76.36098480245). 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 $\frac{N}{d} = D$ )

5831 / 1 = 5831 (the remainder is 0, so 1 and 5831 are divisors of 5831)
5831 / 2 = 2915.5 (the remainder is 1, so 2 is not a divisor of 5831)
5831 / 3 = 1943.6666666667 (the remainder is 2, so 3 is not a divisor of 5831)
...
5831 / 75 = 77.746666666667 (the remainder is 56, so 75 is not a divisor of 5831)
5831 / 76 = 76.723684210526 (the remainder is 55, so 76 is not a divisor of 5831)