What are the divisors of 2284?

1, 2, 4, 571, 1142, 2284

There is a total of 6 positive divisors.
The sum of these divisors is 4004.
The arithmetic mean is 667.33333333333.

4 even divisors

2, 4, 1142, 2284

2 odd divisors

1, 571

How to compute the divisors of 2284?

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 2284 by each of the numbers from 1 to 2284 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)

2284 / 1 = 2284 (the remainder is 0, so 1 is a divisor of 2284)
2284 / 2 = 1142 (the remainder is 0, so 2 is a divisor of 2284)
2284 / 3 = 761.33333333333 (the remainder is 1, so 3 is not a divisor of 2284)
...
2284 / 2283 = 1.0004380201489 (the remainder is 1, so 2283 is not a divisor of 2284)
2284 / 2284 = 1 (the remainder is 0, so 2284 is a divisor of 2284)

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 2284 (i.e. 47.791212581394). 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 $\frac{N}{d} = D$ )

2284 / 1 = 2284 (the remainder is 0, so 1 and 2284 are divisors of 2284)
2284 / 2 = 1142 (the remainder is 0, so 2 and 1142 are divisors of 2284)
2284 / 3 = 761.33333333333 (the remainder is 1, so 3 is not a divisor of 2284)
...
2284 / 46 = 49.652173913043 (the remainder is 30, so 46 is not a divisor of 2284)
2284 / 47 = 48.595744680851 (the remainder is 28, so 47 is not a divisor of 2284)