What are the divisors of 8258?

1, 2, 4129, 8258

There is a total of 4 positive divisors.
The sum of these divisors is 12390.
The arithmetic mean is 3097.5.

2 even divisors

2, 8258

2 odd divisors

1, 4129

How to compute the divisors of 8258?

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 8258 by each of the numbers from 1 to 8258 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)

8258 / 1 = 8258 (the remainder is 0, so 1 is a divisor of 8258)
8258 / 2 = 4129 (the remainder is 0, so 2 is a divisor of 8258)
8258 / 3 = 2752.6666666667 (the remainder is 2, so 3 is not a divisor of 8258)
...
8258 / 8257 = 1.0001211093618 (the remainder is 1, so 8257 is not a divisor of 8258)
8258 / 8258 = 1 (the remainder is 0, so 8258 is a divisor of 8258)

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 8258 (i.e. 90.873538502691). 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 $\frac{N}{d} = D$ )

8258 / 1 = 8258 (the remainder is 0, so 1 and 8258 are divisors of 8258)
8258 / 2 = 4129 (the remainder is 0, so 2 and 4129 are divisors of 8258)
8258 / 3 = 2752.6666666667 (the remainder is 2, so 3 is not a divisor of 8258)
...
8258 / 89 = 92.786516853933 (the remainder is 70, so 89 is not a divisor of 8258)
8258 / 90 = 91.755555555556 (the remainder is 68, so 90 is not a divisor of 8258)