What are the divisors of 2324?

1, 2, 4, 7, 14, 28, 83, 166, 332, 581, 1162, 2324

There is a total of 12 positive divisors.
The sum of these divisors is 4704.
The arithmetic mean is 392.

8 even divisors

2, 4, 14, 28, 166, 332, 1162, 2324

4 odd divisors

1, 7, 83, 581

How to compute the divisors of 2324?

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 2324 by each of the numbers from 1 to 2324 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)

2324 / 1 = 2324 (the remainder is 0, so 1 is a divisor of 2324)
2324 / 2 = 1162 (the remainder is 0, so 2 is a divisor of 2324)
2324 / 3 = 774.66666666667 (the remainder is 2, so 3 is not a divisor of 2324)
...
2324 / 2323 = 1.0004304778304 (the remainder is 1, so 2323 is not a divisor of 2324)
2324 / 2324 = 1 (the remainder is 0, so 2324 is a divisor of 2324)

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 2324 (i.e. 48.207883172776). 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 $\frac{N}{d} = D$ )

2324 / 1 = 2324 (the remainder is 0, so 1 and 2324 are divisors of 2324)
2324 / 2 = 1162 (the remainder is 0, so 2 and 1162 are divisors of 2324)
2324 / 3 = 774.66666666667 (the remainder is 2, so 3 is not a divisor of 2324)
...
2324 / 47 = 49.446808510638 (the remainder is 21, so 47 is not a divisor of 2324)
2324 / 48 = 48.416666666667 (the remainder is 20, so 48 is not a divisor of 2324)