What are the divisors of 2367?

1, 3, 9, 263, 789, 2367

There is a total of 6 positive divisors.
The sum of these divisors is 3432.
The arithmetic mean is 572.

6 odd divisors

1, 3, 9, 263, 789, 2367

How to compute the divisors of 2367?

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 2367 by each of the numbers from 1 to 2367 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)

2367 / 1 = 2367 (the remainder is 0, so 1 is a divisor of 2367)
2367 / 2 = 1183.5 (the remainder is 1, so 2 is not a divisor of 2367)
2367 / 3 = 789 (the remainder is 0, so 3 is a divisor of 2367)
...
2367 / 2366 = 1.0004226542688 (the remainder is 1, so 2366 is not a divisor of 2367)
2367 / 2367 = 1 (the remainder is 0, so 2367 is a divisor of 2367)

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 2367 (i.e. 48.651824220681). 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 $\frac{N}{d} = D$ )

2367 / 1 = 2367 (the remainder is 0, so 1 and 2367 are divisors of 2367)
2367 / 2 = 1183.5 (the remainder is 1, so 2 is not a divisor of 2367)
2367 / 3 = 789 (the remainder is 0, so 3 and 789 are divisors of 2367)
...
2367 / 47 = 50.36170212766 (the remainder is 17, so 47 is not a divisor of 2367)
2367 / 48 = 49.3125 (the remainder is 15, so 48 is not a divisor of 2367)