What are the divisors of 2349?

1, 3, 9, 27, 29, 81, 87, 261, 783, 2349

There is a total of 10 positive divisors.
The sum of these divisors is 3630.
The arithmetic mean is 363.

10 odd divisors

1, 3, 9, 27, 29, 81, 87, 261, 783, 2349

How to compute the divisors of 2349?

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 2349 by each of the numbers from 1 to 2349 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)

2349 / 1 = 2349 (the remainder is 0, so 1 is a divisor of 2349)
2349 / 2 = 1174.5 (the remainder is 1, so 2 is not a divisor of 2349)
2349 / 3 = 783 (the remainder is 0, so 3 is a divisor of 2349)
...
2349 / 2348 = 1.0004258943782 (the remainder is 1, so 2348 is not a divisor of 2349)
2349 / 2349 = 1 (the remainder is 0, so 2349 is a divisor of 2349)

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 2349 (i.e. 48.466483264211). 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 $\frac{N}{d} = D$ )

2349 / 1 = 2349 (the remainder is 0, so 1 and 2349 are divisors of 2349)
2349 / 2 = 1174.5 (the remainder is 1, so 2 is not a divisor of 2349)
2349 / 3 = 783 (the remainder is 0, so 3 and 783 are divisors of 2349)
...
2349 / 47 = 49.978723404255 (the remainder is 46, so 47 is not a divisor of 2349)
2349 / 48 = 48.9375 (the remainder is 45, so 48 is not a divisor of 2349)