What are the divisors of 5825?

1, 5, 25, 233, 1165, 5825

There is a total of 6 positive divisors.
The sum of these divisors is 7254.
The arithmetic mean is 1209.

6 odd divisors

1, 5, 25, 233, 1165, 5825

How to compute the divisors of 5825?

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 5825 by each of the numbers from 1 to 5825 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)

5825 / 1 = 5825 (the remainder is 0, so 1 is a divisor of 5825)
5825 / 2 = 2912.5 (the remainder is 1, so 2 is not a divisor of 5825)
5825 / 3 = 1941.6666666667 (the remainder is 2, so 3 is not a divisor of 5825)
...
5825 / 5824 = 1.0001717032967 (the remainder is 1, so 5824 is not a divisor of 5825)
5825 / 5825 = 1 (the remainder is 0, so 5825 is a divisor of 5825)

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 5825 (i.e. 76.321687612369). 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 $\frac{N}{d} = D$ )

5825 / 1 = 5825 (the remainder is 0, so 1 and 5825 are divisors of 5825)
5825 / 2 = 2912.5 (the remainder is 1, so 2 is not a divisor of 5825)
5825 / 3 = 1941.6666666667 (the remainder is 2, so 3 is not a divisor of 5825)
...
5825 / 75 = 77.666666666667 (the remainder is 50, so 75 is not a divisor of 5825)
5825 / 76 = 76.644736842105 (the remainder is 49, so 76 is not a divisor of 5825)