What are the divisors of 2286?

1, 2, 3, 6, 9, 18, 127, 254, 381, 762, 1143, 2286

There is a total of 12 positive divisors.
The sum of these divisors is 4992.
The arithmetic mean is 416.

6 even divisors

2, 6, 18, 254, 762, 2286

6 odd divisors

1, 3, 9, 127, 381, 1143

How to compute the divisors of 2286?

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 2286 by each of the numbers from 1 to 2286 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)

2286 / 1 = 2286 (the remainder is 0, so 1 is a divisor of 2286)
2286 / 2 = 1143 (the remainder is 0, so 2 is a divisor of 2286)
2286 / 3 = 762 (the remainder is 0, so 3 is a divisor of 2286)
...
2286 / 2285 = 1.0004376367615 (the remainder is 1, so 2285 is not a divisor of 2286)
2286 / 2286 = 1 (the remainder is 0, so 2286 is a divisor of 2286)

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 2286 (i.e. 47.812132351528). 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 $\frac{N}{d} = D$ )

2286 / 1 = 2286 (the remainder is 0, so 1 and 2286 are divisors of 2286)
2286 / 2 = 1143 (the remainder is 0, so 2 and 1143 are divisors of 2286)
2286 / 3 = 762 (the remainder is 0, so 3 and 762 are divisors of 2286)
...
2286 / 46 = 49.695652173913 (the remainder is 32, so 46 is not a divisor of 2286)
2286 / 47 = 48.63829787234 (the remainder is 30, so 47 is not a divisor of 2286)