What are the divisors of 5827?

1, 5827

There is a total of 2 positive divisors.
The sum of these divisors is 5828.
The arithmetic mean is 2914.

2 odd divisors

1, 5827

How to compute the divisors of 5827?

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 5827 by each of the numbers from 1 to 5827 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)

5827 / 1 = 5827 (the remainder is 0, so 1 is a divisor of 5827)
5827 / 2 = 2913.5 (the remainder is 1, so 2 is not a divisor of 5827)
5827 / 3 = 1942.3333333333 (the remainder is 1, so 3 is not a divisor of 5827)
...
5827 / 5826 = 1.0001716443529 (the remainder is 1, so 5826 is not a divisor of 5827)
5827 / 5827 = 1 (the remainder is 0, so 5827 is a divisor of 5827)

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 5827 (i.e. 76.334788923531). 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 $\frac{N}{d} = D$ )

5827 / 1 = 5827 (the remainder is 0, so 1 and 5827 are divisors of 5827)
5827 / 2 = 2913.5 (the remainder is 1, so 2 is not a divisor of 5827)
5827 / 3 = 1942.3333333333 (the remainder is 1, so 3 is not a divisor of 5827)
...
5827 / 75 = 77.693333333333 (the remainder is 52, so 75 is not a divisor of 5827)
5827 / 76 = 76.671052631579 (the remainder is 51, so 76 is not a divisor of 5827)