What are the divisors of 2346?

1, 2, 3, 6, 17, 23, 34, 46, 51, 69, 102, 138, 391, 782, 1173, 2346

There is a total of 16 positive divisors.
The sum of these divisors is 5184.
The arithmetic mean is 324.

8 even divisors

2, 6, 34, 46, 102, 138, 782, 2346

8 odd divisors

1, 3, 17, 23, 51, 69, 391, 1173

How to compute the divisors of 2346?

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 2346 by each of the numbers from 1 to 2346 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)

2346 / 1 = 2346 (the remainder is 0, so 1 is a divisor of 2346)
2346 / 2 = 1173 (the remainder is 0, so 2 is a divisor of 2346)
2346 / 3 = 782 (the remainder is 0, so 3 is a divisor of 2346)
...
2346 / 2345 = 1.0004264392324 (the remainder is 1, so 2345 is not a divisor of 2346)
2346 / 2346 = 1 (the remainder is 0, so 2346 is a divisor of 2346)

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 2346 (i.e. 48.435524153249). 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 $\frac{N}{d} = D$ )

2346 / 1 = 2346 (the remainder is 0, so 1 and 2346 are divisors of 2346)
2346 / 2 = 1173 (the remainder is 0, so 2 and 1173 are divisors of 2346)
2346 / 3 = 782 (the remainder is 0, so 3 and 782 are divisors of 2346)
...
2346 / 47 = 49.914893617021 (the remainder is 43, so 47 is not a divisor of 2346)
2346 / 48 = 48.875 (the remainder is 42, so 48 is not a divisor of 2346)