What are the divisors of 2288?

1, 2, 4, 8, 11, 13, 16, 22, 26, 44, 52, 88, 104, 143, 176, 208, 286, 572, 1144, 2288

There is a total of 20 positive divisors.
The sum of these divisors is 5208.
The arithmetic mean is 260.4.

16 even divisors

2, 4, 8, 16, 22, 26, 44, 52, 88, 104, 176, 208, 286, 572, 1144, 2288

4 odd divisors

1, 11, 13, 143

How to compute the divisors of 2288?

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 2288 by each of the numbers from 1 to 2288 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)

2288 / 1 = 2288 (the remainder is 0, so 1 is a divisor of 2288)
2288 / 2 = 1144 (the remainder is 0, so 2 is a divisor of 2288)
2288 / 3 = 762.66666666667 (the remainder is 2, so 3 is not a divisor of 2288)
...
2288 / 2287 = 1.0004372540446 (the remainder is 1, so 2287 is not a divisor of 2288)
2288 / 2288 = 1 (the remainder is 0, so 2288 is a divisor of 2288)

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 2288 (i.e. 47.833042972406). 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 $\frac{N}{d} = D$ )

2288 / 1 = 2288 (the remainder is 0, so 1 and 2288 are divisors of 2288)
2288 / 2 = 1144 (the remainder is 0, so 2 and 1144 are divisors of 2288)
2288 / 3 = 762.66666666667 (the remainder is 2, so 3 is not a divisor of 2288)
...
2288 / 46 = 49.739130434783 (the remainder is 34, so 46 is not a divisor of 2288)
2288 / 47 = 48.68085106383 (the remainder is 32, so 47 is not a divisor of 2288)