What are the divisors of 5847?

1, 3, 1949, 5847

There is a total of 4 positive divisors.
The sum of these divisors is 7800.
The arithmetic mean is 1950.

4 odd divisors

1, 3, 1949, 5847

How to compute the divisors of 5847?

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 5847 by each of the numbers from 1 to 5847 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)

5847 / 1 = 5847 (the remainder is 0, so 1 is a divisor of 5847)
5847 / 2 = 2923.5 (the remainder is 1, so 2 is not a divisor of 5847)
5847 / 3 = 1949 (the remainder is 0, so 3 is a divisor of 5847)
...
5847 / 5846 = 1.0001710571331 (the remainder is 1, so 5846 is not a divisor of 5847)
5847 / 5847 = 1 (the remainder is 0, so 5847 is a divisor of 5847)

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 5847 (i.e. 76.465678575424). 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 $\frac{N}{d} = D$ )

5847 / 1 = 5847 (the remainder is 0, so 1 and 5847 are divisors of 5847)
5847 / 2 = 2923.5 (the remainder is 1, so 2 is not a divisor of 5847)
5847 / 3 = 1949 (the remainder is 0, so 3 and 1949 are divisors of 5847)
...
5847 / 75 = 77.96 (the remainder is 72, so 75 is not a divisor of 5847)
5847 / 76 = 76.934210526316 (the remainder is 71, so 76 is not a divisor of 5847)