What are the divisors of 2266?

1, 2, 11, 22, 103, 206, 1133, 2266

There is a total of 8 positive divisors.
The sum of these divisors is 3744.
The arithmetic mean is 468.

4 even divisors

2, 22, 206, 2266

4 odd divisors

1, 11, 103, 1133

How to compute the divisors of 2266?

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 2266 by each of the numbers from 1 to 2266 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)

2266 / 1 = 2266 (the remainder is 0, so 1 is a divisor of 2266)
2266 / 2 = 1133 (the remainder is 0, so 2 is a divisor of 2266)
2266 / 3 = 755.33333333333 (the remainder is 1, so 3 is not a divisor of 2266)
...
2266 / 2265 = 1.0004415011038 (the remainder is 1, so 2265 is not a divisor of 2266)
2266 / 2266 = 1 (the remainder is 0, so 2266 is a divisor of 2266)

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 2266 (i.e. 47.602520941648). 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 $\frac{N}{d} = D$ )

2266 / 1 = 2266 (the remainder is 0, so 1 and 2266 are divisors of 2266)
2266 / 2 = 1133 (the remainder is 0, so 2 and 1133 are divisors of 2266)
2266 / 3 = 755.33333333333 (the remainder is 1, so 3 is not a divisor of 2266)
...
2266 / 46 = 49.260869565217 (the remainder is 12, so 46 is not a divisor of 2266)
2266 / 47 = 48.212765957447 (the remainder is 10, so 47 is not a divisor of 2266)