What are the divisors of 5943?

1, 3, 7, 21, 283, 849, 1981, 5943

There is a total of 8 positive divisors.
The sum of these divisors is 9088.
The arithmetic mean is 1136.

8 odd divisors

1, 3, 7, 21, 283, 849, 1981, 5943

How to compute the divisors of 5943?

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 5943 by each of the numbers from 1 to 5943 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)

5943 / 1 = 5943 (the remainder is 0, so 1 is a divisor of 5943)
5943 / 2 = 2971.5 (the remainder is 1, so 2 is not a divisor of 5943)
5943 / 3 = 1981 (the remainder is 0, so 3 is a divisor of 5943)
...
5943 / 5942 = 1.0001682935039 (the remainder is 1, so 5942 is not a divisor of 5943)
5943 / 5943 = 1 (the remainder is 0, so 5943 is a divisor of 5943)

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 5943 (i.e. 77.090855488832). 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 $\frac{N}{d} = D$ )

5943 / 1 = 5943 (the remainder is 0, so 1 and 5943 are divisors of 5943)
5943 / 2 = 2971.5 (the remainder is 1, so 2 is not a divisor of 5943)
5943 / 3 = 1981 (the remainder is 0, so 3 and 1981 are divisors of 5943)
...
5943 / 76 = 78.197368421053 (the remainder is 15, so 76 is not a divisor of 5943)
5943 / 77 = 77.181818181818 (the remainder is 14, so 77 is not a divisor of 5943)