What are the divisors of 322?

1, 2, 7, 14, 23, 46, 161, 322

There is a total of 8 positive divisors.
The sum of these divisors is 576.
The arithmetic mean is 72.

4 even divisors

2, 14, 46, 322

4 odd divisors

1, 7, 23, 161

How to compute the divisors of 322?

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 322 by each of the numbers from 1 to 322 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)

322 / 1 = 322 (the remainder is 0, so 1 is a divisor of 322)
322 / 2 = 161 (the remainder is 0, so 2 is a divisor of 322)
322 / 3 = 107.33333333333 (the remainder is 1, so 3 is not a divisor of 322)
...
322 / 321 = 1.0031152647975 (the remainder is 1, so 321 is not a divisor of 322)
322 / 322 = 1 (the remainder is 0, so 322 is a divisor of 322)

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 322 (i.e. 17.944358444926). 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 $\frac{N}{d} = D$ )

322 / 1 = 322 (the remainder is 0, so 1 and 322 are divisors of 322)
322 / 2 = 161 (the remainder is 0, so 2 and 161 are divisors of 322)
322 / 3 = 107.33333333333 (the remainder is 1, so 3 is not a divisor of 322)
...
322 / 16 = 20.125 (the remainder is 2, so 16 is not a divisor of 322)
322 / 17 = 18.941176470588 (the remainder is 16, so 17 is not a divisor of 322)