What are the divisors of 2259?

1, 3, 9, 251, 753, 2259

There is a total of 6 positive divisors.
The sum of these divisors is 3276.
The arithmetic mean is 546.

6 odd divisors

1, 3, 9, 251, 753, 2259

How to compute the divisors of 2259?

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 2259 by each of the numbers from 1 to 2259 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)

2259 / 1 = 2259 (the remainder is 0, so 1 is a divisor of 2259)
2259 / 2 = 1129.5 (the remainder is 1, so 2 is not a divisor of 2259)
2259 / 3 = 753 (the remainder is 0, so 3 is a divisor of 2259)
...
2259 / 2258 = 1.0004428697963 (the remainder is 1, so 2258 is not a divisor of 2259)
2259 / 2259 = 1 (the remainder is 0, so 2259 is a divisor of 2259)

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 2259 (i.e. 47.528938553265). 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 $\frac{N}{d} = D$ )

2259 / 1 = 2259 (the remainder is 0, so 1 and 2259 are divisors of 2259)
2259 / 2 = 1129.5 (the remainder is 1, so 2 is not a divisor of 2259)
2259 / 3 = 753 (the remainder is 0, so 3 and 753 are divisors of 2259)
...
2259 / 46 = 49.108695652174 (the remainder is 5, so 46 is not a divisor of 2259)
2259 / 47 = 48.063829787234 (the remainder is 3, so 47 is not a divisor of 2259)