What are the divisors of 2305?

1, 5, 461, 2305

There is a total of 4 positive divisors.
The sum of these divisors is 2772.
The arithmetic mean is 693.

4 odd divisors

1, 5, 461, 2305

How to compute the divisors of 2305?

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 2305 by each of the numbers from 1 to 2305 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)

2305 / 1 = 2305 (the remainder is 0, so 1 is a divisor of 2305)
2305 / 2 = 1152.5 (the remainder is 1, so 2 is not a divisor of 2305)
2305 / 3 = 768.33333333333 (the remainder is 1, so 3 is not a divisor of 2305)
...
2305 / 2304 = 1.0004340277778 (the remainder is 1, so 2304 is not a divisor of 2305)
2305 / 2305 = 1 (the remainder is 0, so 2305 is a divisor of 2305)

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 2305 (i.e. 48.010415536631). 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 $\frac{N}{d} = D$ )

2305 / 1 = 2305 (the remainder is 0, so 1 and 2305 are divisors of 2305)
2305 / 2 = 1152.5 (the remainder is 1, so 2 is not a divisor of 2305)
2305 / 3 = 768.33333333333 (the remainder is 1, so 3 is not a divisor of 2305)
...
2305 / 47 = 49.042553191489 (the remainder is 2, so 47 is not a divisor of 2305)
2305 / 48 = 48.020833333333 (the remainder is 1, so 48 is not a divisor of 2305)