What are the divisors of 239?

1, 239

There is a total of 2 positive divisors.
The sum of these divisors is 240.
The arithmetic mean is 120.

2 odd divisors

1, 239

How to compute the divisors of 239?

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 239 by each of the numbers from 1 to 239 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)

239 / 1 = 239 (the remainder is 0, so 1 is a divisor of 239)
239 / 2 = 119.5 (the remainder is 1, so 2 is not a divisor of 239)
239 / 3 = 79.666666666667 (the remainder is 2, so 3 is not a divisor of 239)
...
239 / 238 = 1.0042016806723 (the remainder is 1, so 238 is not a divisor of 239)
239 / 239 = 1 (the remainder is 0, so 239 is a divisor of 239)

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 239 (i.e. 15.45962483374). 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 $\frac{N}{d} = D$ )

239 / 1 = 239 (the remainder is 0, so 1 and 239 are divisors of 239)
239 / 2 = 119.5 (the remainder is 1, so 2 is not a divisor of 239)
239 / 3 = 79.666666666667 (the remainder is 2, so 3 is not a divisor of 239)
...
239 / 14 = 17.071428571429 (the remainder is 1, so 14 is not a divisor of 239)
239 / 15 = 15.933333333333 (the remainder is 14, so 15 is not a divisor of 239)