What are the divisors of 5846?

1, 2, 37, 74, 79, 158, 2923, 5846

There is a total of 8 positive divisors.
The sum of these divisors is 9120.
The arithmetic mean is 1140.

4 even divisors

2, 74, 158, 5846

4 odd divisors

1, 37, 79, 2923

How to compute the divisors of 5846?

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 5846 by each of the numbers from 1 to 5846 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)

5846 / 1 = 5846 (the remainder is 0, so 1 is a divisor of 5846)
5846 / 2 = 2923 (the remainder is 0, so 2 is a divisor of 5846)
5846 / 3 = 1948.6666666667 (the remainder is 2, so 3 is not a divisor of 5846)
...
5846 / 5845 = 1.0001710863986 (the remainder is 1, so 5845 is not a divisor of 5846)
5846 / 5846 = 1 (the remainder is 0, so 5846 is a divisor of 5846)

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 5846 (i.e. 76.459139414461). 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 $\frac{N}{d} = D$ )

5846 / 1 = 5846 (the remainder is 0, so 1 and 5846 are divisors of 5846)
5846 / 2 = 2923 (the remainder is 0, so 2 and 2923 are divisors of 5846)
5846 / 3 = 1948.6666666667 (the remainder is 2, so 3 is not a divisor of 5846)
...
5846 / 75 = 77.946666666667 (the remainder is 71, so 75 is not a divisor of 5846)
5846 / 76 = 76.921052631579 (the remainder is 70, so 76 is not a divisor of 5846)