What are the divisors of 2344?

1, 2, 4, 8, 293, 586, 1172, 2344

There is a total of 8 positive divisors.
The sum of these divisors is 4410.
The arithmetic mean is 551.25.

6 even divisors

2, 4, 8, 586, 1172, 2344

2 odd divisors

1, 293

How to compute the divisors of 2344?

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 2344 by each of the numbers from 1 to 2344 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)

2344 / 1 = 2344 (the remainder is 0, so 1 is a divisor of 2344)
2344 / 2 = 1172 (the remainder is 0, so 2 is a divisor of 2344)
2344 / 3 = 781.33333333333 (the remainder is 1, so 3 is not a divisor of 2344)
...
2344 / 2343 = 1.0004268032437 (the remainder is 1, so 2343 is not a divisor of 2344)
2344 / 2344 = 1 (the remainder is 0, so 2344 is a divisor of 2344)

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 2344 (i.e. 48.414873747641). 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 $\frac{N}{d} = D$ )

2344 / 1 = 2344 (the remainder is 0, so 1 and 2344 are divisors of 2344)
2344 / 2 = 1172 (the remainder is 0, so 2 and 1172 are divisors of 2344)
2344 / 3 = 781.33333333333 (the remainder is 1, so 3 is not a divisor of 2344)
...
2344 / 47 = 49.872340425532 (the remainder is 41, so 47 is not a divisor of 2344)
2344 / 48 = 48.833333333333 (the remainder is 40, so 48 is not a divisor of 2344)