What are the divisors of 237?

1, 3, 79, 237

There is a total of 4 positive divisors.
The sum of these divisors is 320.
The arithmetic mean is 80.

4 odd divisors

1, 3, 79, 237

How to compute the divisors of 237?

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 237 by each of the numbers from 1 to 237 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)

237 / 1 = 237 (the remainder is 0, so 1 is a divisor of 237)
237 / 2 = 118.5 (the remainder is 1, so 2 is not a divisor of 237)
237 / 3 = 79 (the remainder is 0, so 3 is a divisor of 237)
...
237 / 236 = 1.0042372881356 (the remainder is 1, so 236 is not a divisor of 237)
237 / 237 = 1 (the remainder is 0, so 237 is a divisor of 237)

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 237 (i.e. 15.394804318341). 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 $\frac{N}{d} = D$ )

237 / 1 = 237 (the remainder is 0, so 1 and 237 are divisors of 237)
237 / 2 = 118.5 (the remainder is 1, so 2 is not a divisor of 237)
237 / 3 = 79 (the remainder is 0, so 3 and 79 are divisors of 237)
...
237 / 14 = 16.928571428571 (the remainder is 13, so 14 is not a divisor of 237)
237 / 15 = 15.8 (the remainder is 12, so 15 is not a divisor of 237)