What are the divisors of 326?

1, 2, 163, 326

There is a total of 4 positive divisors.
The sum of these divisors is 492.
The arithmetic mean is 123.

2 even divisors

2, 326

2 odd divisors

1, 163

How to compute the divisors of 326?

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 326 by each of the numbers from 1 to 326 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)

326 / 1 = 326 (the remainder is 0, so 1 is a divisor of 326)
326 / 2 = 163 (the remainder is 0, so 2 is a divisor of 326)
326 / 3 = 108.66666666667 (the remainder is 2, so 3 is not a divisor of 326)
...
326 / 325 = 1.0030769230769 (the remainder is 1, so 325 is not a divisor of 326)
326 / 326 = 1 (the remainder is 0, so 326 is a divisor of 326)

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 326 (i.e. 18.055470085268). 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 $\frac{N}{d} = D$ )

326 / 1 = 326 (the remainder is 0, so 1 and 326 are divisors of 326)
326 / 2 = 163 (the remainder is 0, so 2 and 163 are divisors of 326)
326 / 3 = 108.66666666667 (the remainder is 2, so 3 is not a divisor of 326)
...
326 / 17 = 19.176470588235 (the remainder is 3, so 17 is not a divisor of 326)
326 / 18 = 18.111111111111 (the remainder is 2, so 18 is not a divisor of 326)