What are the divisors of 258?

1, 2, 3, 6, 43, 86, 129, 258

There is a total of 8 positive divisors.
The sum of these divisors is 528.
The arithmetic mean is 66.

4 even divisors

2, 6, 86, 258

4 odd divisors

1, 3, 43, 129

How to compute the divisors of 258?

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 258 by each of the numbers from 1 to 258 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)

258 / 1 = 258 (the remainder is 0, so 1 is a divisor of 258)
258 / 2 = 129 (the remainder is 0, so 2 is a divisor of 258)
258 / 3 = 86 (the remainder is 0, so 3 is a divisor of 258)
...
258 / 257 = 1.0038910505837 (the remainder is 1, so 257 is not a divisor of 258)
258 / 258 = 1 (the remainder is 0, so 258 is a divisor of 258)

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 258 (i.e. 16.062378404209). 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 $\frac{N}{d} = D$ )

258 / 1 = 258 (the remainder is 0, so 1 and 258 are divisors of 258)
258 / 2 = 129 (the remainder is 0, so 2 and 129 are divisors of 258)
258 / 3 = 86 (the remainder is 0, so 3 and 86 are divisors of 258)
...
258 / 15 = 17.2 (the remainder is 3, so 15 is not a divisor of 258)
258 / 16 = 16.125 (the remainder is 2, so 16 is not a divisor of 258)