What are the divisors of 2386?

1, 2, 1193, 2386

There is a total of 4 positive divisors.
The sum of these divisors is 3582.
The arithmetic mean is 895.5.

2 even divisors

2, 2386

2 odd divisors

1, 1193

How to compute the divisors of 2386?

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 2386 by each of the numbers from 1 to 2386 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)

2386 / 1 = 2386 (the remainder is 0, so 1 is a divisor of 2386)
2386 / 2 = 1193 (the remainder is 0, so 2 is a divisor of 2386)
2386 / 3 = 795.33333333333 (the remainder is 1, so 3 is not a divisor of 2386)
...
2386 / 2385 = 1.0004192872117 (the remainder is 1, so 2385 is not a divisor of 2386)
2386 / 2386 = 1 (the remainder is 0, so 2386 is a divisor of 2386)

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 2386 (i.e. 48.846698967279). 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 $\frac{N}{d} = D$ )

2386 / 1 = 2386 (the remainder is 0, so 1 and 2386 are divisors of 2386)
2386 / 2 = 1193 (the remainder is 0, so 2 and 1193 are divisors of 2386)
2386 / 3 = 795.33333333333 (the remainder is 1, so 3 is not a divisor of 2386)
...
2386 / 47 = 50.765957446809 (the remainder is 36, so 47 is not a divisor of 2386)
2386 / 48 = 49.708333333333 (the remainder is 34, so 48 is not a divisor of 2386)