What are the divisors of 5859?

1, 3, 7, 9, 21, 27, 31, 63, 93, 189, 217, 279, 651, 837, 1953, 5859

There is a total of 16 positive divisors.
The sum of these divisors is 10240.
The arithmetic mean is 640.

16 odd divisors

1, 3, 7, 9, 21, 27, 31, 63, 93, 189, 217, 279, 651, 837, 1953, 5859

How to compute the divisors of 5859?

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 5859 by each of the numbers from 1 to 5859 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)

5859 / 1 = 5859 (the remainder is 0, so 1 is a divisor of 5859)
5859 / 2 = 2929.5 (the remainder is 1, so 2 is not a divisor of 5859)
5859 / 3 = 1953 (the remainder is 0, so 3 is a divisor of 5859)
...
5859 / 5858 = 1.0001707067258 (the remainder is 1, so 5858 is not a divisor of 5859)
5859 / 5859 = 1 (the remainder is 0, so 5859 is a divisor of 5859)

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 5859 (i.e. 76.544104933038). 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 $\frac{N}{d} = D$ )

5859 / 1 = 5859 (the remainder is 0, so 1 and 5859 are divisors of 5859)
5859 / 2 = 2929.5 (the remainder is 1, so 2 is not a divisor of 5859)
5859 / 3 = 1953 (the remainder is 0, so 3 and 1953 are divisors of 5859)
...
5859 / 75 = 78.12 (the remainder is 9, so 75 is not a divisor of 5859)
5859 / 76 = 77.092105263158 (the remainder is 7, so 76 is not a divisor of 5859)