What are the divisors of 5258?

1, 2, 11, 22, 239, 478, 2629, 5258

There is a total of 8 positive divisors.
The sum of these divisors is 8640.
The arithmetic mean is 1080.

4 even divisors

2, 22, 478, 5258

4 odd divisors

1, 11, 239, 2629

How to compute the divisors of 5258?

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 5258 by each of the numbers from 1 to 5258 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)

5258 / 1 = 5258 (the remainder is 0, so 1 is a divisor of 5258)
5258 / 2 = 2629 (the remainder is 0, so 2 is a divisor of 5258)
5258 / 3 = 1752.6666666667 (the remainder is 2, so 3 is not a divisor of 5258)
...
5258 / 5257 = 1.0001902225604 (the remainder is 1, so 5257 is not a divisor of 5258)
5258 / 5258 = 1 (the remainder is 0, so 5258 is a divisor of 5258)

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 5258 (i.e. 72.512067961133). 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 $\frac{N}{d} = D$ )

5258 / 1 = 5258 (the remainder is 0, so 1 and 5258 are divisors of 5258)
5258 / 2 = 2629 (the remainder is 0, so 2 and 2629 are divisors of 5258)
5258 / 3 = 1752.6666666667 (the remainder is 2, so 3 is not a divisor of 5258)
...
5258 / 71 = 74.056338028169 (the remainder is 4, so 71 is not a divisor of 5258)
5258 / 72 = 73.027777777778 (the remainder is 2, so 72 is not a divisor of 5258)