What are the divisors of 235?

1, 5, 47, 235

There is a total of 4 positive divisors.
The sum of these divisors is 288.
The arithmetic mean is 72.

4 odd divisors

1, 5, 47, 235

How to compute the divisors of 235?

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 235 by each of the numbers from 1 to 235 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)

235 / 1 = 235 (the remainder is 0, so 1 is a divisor of 235)
235 / 2 = 117.5 (the remainder is 1, so 2 is not a divisor of 235)
235 / 3 = 78.333333333333 (the remainder is 1, so 3 is not a divisor of 235)
...
235 / 234 = 1.0042735042735 (the remainder is 1, so 234 is not a divisor of 235)
235 / 235 = 1 (the remainder is 0, so 235 is a divisor of 235)

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 235 (i.e. 15.329709716756). 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 $\frac{N}{d} = D$ )

235 / 1 = 235 (the remainder is 0, so 1 and 235 are divisors of 235)
235 / 2 = 117.5 (the remainder is 1, so 2 is not a divisor of 235)
235 / 3 = 78.333333333333 (the remainder is 1, so 3 is not a divisor of 235)
...
235 / 14 = 16.785714285714 (the remainder is 11, so 14 is not a divisor of 235)
235 / 15 = 15.666666666667 (the remainder is 10, so 15 is not a divisor of 235)