What are the divisors of 236?

1, 2, 4, 59, 118, 236

There is a total of 6 positive divisors.
The sum of these divisors is 420.
The arithmetic mean is 70.

4 even divisors

2, 4, 118, 236

2 odd divisors

1, 59

How to compute the divisors of 236?

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 236 by each of the numbers from 1 to 236 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)

236 / 1 = 236 (the remainder is 0, so 1 is a divisor of 236)
236 / 2 = 118 (the remainder is 0, so 2 is a divisor of 236)
236 / 3 = 78.666666666667 (the remainder is 2, so 3 is not a divisor of 236)
...
236 / 235 = 1.0042553191489 (the remainder is 1, so 235 is not a divisor of 236)
236 / 236 = 1 (the remainder is 0, so 236 is a divisor of 236)

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 236 (i.e. 15.362291495737). 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 $\frac{N}{d} = D$ )

236 / 1 = 236 (the remainder is 0, so 1 and 236 are divisors of 236)
236 / 2 = 118 (the remainder is 0, so 2 and 118 are divisors of 236)
236 / 3 = 78.666666666667 (the remainder is 2, so 3 is not a divisor of 236)
...
236 / 14 = 16.857142857143 (the remainder is 12, so 14 is not a divisor of 236)
236 / 15 = 15.733333333333 (the remainder is 11, so 15 is not a divisor of 236)