What are the divisors of 5829?

1, 3, 29, 67, 87, 201, 1943, 5829

There is a total of 8 positive divisors.
The sum of these divisors is 8160.
The arithmetic mean is 1020.

8 odd divisors

1, 3, 29, 67, 87, 201, 1943, 5829

How to compute the divisors of 5829?

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 5829 by each of the numbers from 1 to 5829 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)

5829 / 1 = 5829 (the remainder is 0, so 1 is a divisor of 5829)
5829 / 2 = 2914.5 (the remainder is 1, so 2 is not a divisor of 5829)
5829 / 3 = 1943 (the remainder is 0, so 3 is a divisor of 5829)
...
5829 / 5828 = 1.0001715854496 (the remainder is 1, so 5828 is not a divisor of 5829)
5829 / 5829 = 1 (the remainder is 0, so 5829 is a divisor of 5829)

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 5829 (i.e. 76.347887986506). 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 $\frac{N}{d} = D$ )

5829 / 1 = 5829 (the remainder is 0, so 1 and 5829 are divisors of 5829)
5829 / 2 = 2914.5 (the remainder is 1, so 2 is not a divisor of 5829)
5829 / 3 = 1943 (the remainder is 0, so 3 and 1943 are divisors of 5829)
...
5829 / 75 = 77.72 (the remainder is 54, so 75 is not a divisor of 5829)
5829 / 76 = 76.697368421053 (the remainder is 53, so 76 is not a divisor of 5829)