What are the divisors of 5863?

1, 11, 13, 41, 143, 451, 533, 5863

There is a total of 8 positive divisors.
The sum of these divisors is 7056.
The arithmetic mean is 882.

8 odd divisors

1, 11, 13, 41, 143, 451, 533, 5863

How to compute the divisors of 5863?

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 5863 by each of the numbers from 1 to 5863 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)

5863 / 1 = 5863 (the remainder is 0, so 1 is a divisor of 5863)
5863 / 2 = 2931.5 (the remainder is 1, so 2 is not a divisor of 5863)
5863 / 3 = 1954.3333333333 (the remainder is 1, so 3 is not a divisor of 5863)
...
5863 / 5862 = 1.0001705902422 (the remainder is 1, so 5862 is not a divisor of 5863)
5863 / 5863 = 1 (the remainder is 0, so 5863 is a divisor of 5863)

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 5863 (i.e. 76.570229201694). 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 $\frac{N}{d} = D$ )

5863 / 1 = 5863 (the remainder is 0, so 1 and 5863 are divisors of 5863)
5863 / 2 = 2931.5 (the remainder is 1, so 2 is not a divisor of 5863)
5863 / 3 = 1954.3333333333 (the remainder is 1, so 3 is not a divisor of 5863)
...
5863 / 75 = 78.173333333333 (the remainder is 13, so 75 is not a divisor of 5863)
5863 / 76 = 77.144736842105 (the remainder is 11, so 76 is not a divisor of 5863)