What are the divisors of 328?

1, 2, 4, 8, 41, 82, 164, 328

There is a total of 8 positive divisors.
The sum of these divisors is 630.
The arithmetic mean is 78.75.

6 even divisors

2, 4, 8, 82, 164, 328

2 odd divisors

1, 41

How to compute the divisors of 328?

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 328 by each of the numbers from 1 to 328 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)

328 / 1 = 328 (the remainder is 0, so 1 is a divisor of 328)
328 / 2 = 164 (the remainder is 0, so 2 is a divisor of 328)
328 / 3 = 109.33333333333 (the remainder is 1, so 3 is not a divisor of 328)
...
328 / 327 = 1.0030581039755 (the remainder is 1, so 327 is not a divisor of 328)
328 / 328 = 1 (the remainder is 0, so 328 is a divisor of 328)

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 328 (i.e. 18.110770276275). 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 $\frac{N}{d} = D$ )

328 / 1 = 328 (the remainder is 0, so 1 and 328 are divisors of 328)
328 / 2 = 164 (the remainder is 0, so 2 and 164 are divisors of 328)
328 / 3 = 109.33333333333 (the remainder is 1, so 3 is not a divisor of 328)
...
328 / 17 = 19.294117647059 (the remainder is 5, so 17 is not a divisor of 328)
328 / 18 = 18.222222222222 (the remainder is 4, so 18 is not a divisor of 328)