What are the divisors of 2382?

1, 2, 3, 6, 397, 794, 1191, 2382

There is a total of 8 positive divisors.
The sum of these divisors is 4776.
The arithmetic mean is 597.

4 even divisors

2, 6, 794, 2382

4 odd divisors

1, 3, 397, 1191

How to compute the divisors of 2382?

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 2382 by each of the numbers from 1 to 2382 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)

2382 / 1 = 2382 (the remainder is 0, so 1 is a divisor of 2382)
2382 / 2 = 1191 (the remainder is 0, so 2 is a divisor of 2382)
2382 / 3 = 794 (the remainder is 0, so 3 is a divisor of 2382)
...
2382 / 2381 = 1.0004199916002 (the remainder is 1, so 2381 is not a divisor of 2382)
2382 / 2382 = 1 (the remainder is 0, so 2382 is a divisor of 2382)

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 2382 (i.e. 48.80573736765). 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 $\frac{N}{d} = D$ )

2382 / 1 = 2382 (the remainder is 0, so 1 and 2382 are divisors of 2382)
2382 / 2 = 1191 (the remainder is 0, so 2 and 1191 are divisors of 2382)
2382 / 3 = 794 (the remainder is 0, so 3 and 794 are divisors of 2382)
...
2382 / 47 = 50.68085106383 (the remainder is 32, so 47 is not a divisor of 2382)
2382 / 48 = 49.625 (the remainder is 30, so 48 is not a divisor of 2382)