What are the divisors of 2323?

1, 23, 101, 2323

There is a total of 4 positive divisors.
The sum of these divisors is 2448.
The arithmetic mean is 612.

4 odd divisors

1, 23, 101, 2323

How to compute the divisors of 2323?

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 2323 by each of the numbers from 1 to 2323 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)

2323 / 1 = 2323 (the remainder is 0, so 1 is a divisor of 2323)
2323 / 2 = 1161.5 (the remainder is 1, so 2 is not a divisor of 2323)
2323 / 3 = 774.33333333333 (the remainder is 1, so 3 is not a divisor of 2323)
...
2323 / 2322 = 1.0004306632214 (the remainder is 1, so 2322 is not a divisor of 2323)
2323 / 2323 = 1 (the remainder is 0, so 2323 is a divisor of 2323)

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 2323 (i.e. 48.197510309144). 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 $\frac{N}{d} = D$ )

2323 / 1 = 2323 (the remainder is 0, so 1 and 2323 are divisors of 2323)
2323 / 2 = 1161.5 (the remainder is 1, so 2 is not a divisor of 2323)
2323 / 3 = 774.33333333333 (the remainder is 1, so 3 is not a divisor of 2323)
...
2323 / 47 = 49.425531914894 (the remainder is 20, so 47 is not a divisor of 2323)
2323 / 48 = 48.395833333333 (the remainder is 19, so 48 is not a divisor of 2323)