What are the divisors of 339?

1, 3, 113, 339

There is a total of 4 positive divisors.
The sum of these divisors is 456.
The arithmetic mean is 114.

4 odd divisors

1, 3, 113, 339

How to compute the divisors of 339?

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 339 by each of the numbers from 1 to 339 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)

339 / 1 = 339 (the remainder is 0, so 1 is a divisor of 339)
339 / 2 = 169.5 (the remainder is 1, so 2 is not a divisor of 339)
339 / 3 = 113 (the remainder is 0, so 3 is a divisor of 339)
...
339 / 338 = 1.0029585798817 (the remainder is 1, so 338 is not a divisor of 339)
339 / 339 = 1 (the remainder is 0, so 339 is a divisor of 339)

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 339 (i.e. 18.411952639522). 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 $\frac{N}{d} = D$ )

339 / 1 = 339 (the remainder is 0, so 1 and 339 are divisors of 339)
339 / 2 = 169.5 (the remainder is 1, so 2 is not a divisor of 339)
339 / 3 = 113 (the remainder is 0, so 3 and 113 are divisors of 339)
...
339 / 17 = 19.941176470588 (the remainder is 16, so 17 is not a divisor of 339)
339 / 18 = 18.833333333333 (the remainder is 15, so 18 is not a divisor of 339)