What are the divisors of 5817?

1, 3, 7, 21, 277, 831, 1939, 5817

There is a total of 8 positive divisors.
The sum of these divisors is 8896.
The arithmetic mean is 1112.

8 odd divisors

1, 3, 7, 21, 277, 831, 1939, 5817

How to compute the divisors of 5817?

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 5817 by each of the numbers from 1 to 5817 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)

5817 / 1 = 5817 (the remainder is 0, so 1 is a divisor of 5817)
5817 / 2 = 2908.5 (the remainder is 1, so 2 is not a divisor of 5817)
5817 / 3 = 1939 (the remainder is 0, so 3 is a divisor of 5817)
...
5817 / 5816 = 1.0001719394773 (the remainder is 1, so 5816 is not a divisor of 5817)
5817 / 5817 = 1 (the remainder is 0, so 5817 is a divisor of 5817)

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 5817 (i.e. 76.269259862673). 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 $\frac{N}{d} = D$ )

5817 / 1 = 5817 (the remainder is 0, so 1 and 5817 are divisors of 5817)
5817 / 2 = 2908.5 (the remainder is 1, so 2 is not a divisor of 5817)
5817 / 3 = 1939 (the remainder is 0, so 3 and 1939 are divisors of 5817)
...
5817 / 75 = 77.56 (the remainder is 42, so 75 is not a divisor of 5817)
5817 / 76 = 76.539473684211 (the remainder is 41, so 76 is not a divisor of 5817)