What are the divisors of 2283?

1, 3, 761, 2283

There is a total of 4 positive divisors.
The sum of these divisors is 3048.
The arithmetic mean is 762.

4 odd divisors

1, 3, 761, 2283

How to compute the divisors of 2283?

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 2283 by each of the numbers from 1 to 2283 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)

2283 / 1 = 2283 (the remainder is 0, so 1 is a divisor of 2283)
2283 / 2 = 1141.5 (the remainder is 1, so 2 is not a divisor of 2283)
2283 / 3 = 761 (the remainder is 0, so 3 is a divisor of 2283)
...
2283 / 2282 = 1.0004382120947 (the remainder is 1, so 2282 is not a divisor of 2283)
2283 / 2283 = 1 (the remainder is 0, so 2283 is a divisor of 2283)

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 2283 (i.e. 47.780749261601). 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 $\frac{N}{d} = D$ )

2283 / 1 = 2283 (the remainder is 0, so 1 and 2283 are divisors of 2283)
2283 / 2 = 1141.5 (the remainder is 1, so 2 is not a divisor of 2283)
2283 / 3 = 761 (the remainder is 0, so 3 and 761 are divisors of 2283)
...
2283 / 46 = 49.630434782609 (the remainder is 29, so 46 is not a divisor of 2283)
2283 / 47 = 48.574468085106 (the remainder is 27, so 47 is not a divisor of 2283)