What are the divisors of 2385?

1, 3, 5, 9, 15, 45, 53, 159, 265, 477, 795, 2385

There is a total of 12 positive divisors.
The sum of these divisors is 4212.
The arithmetic mean is 351.

12 odd divisors

1, 3, 5, 9, 15, 45, 53, 159, 265, 477, 795, 2385

How to compute the divisors of 2385?

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 2385 by each of the numbers from 1 to 2385 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)

2385 / 1 = 2385 (the remainder is 0, so 1 is a divisor of 2385)
2385 / 2 = 1192.5 (the remainder is 1, so 2 is not a divisor of 2385)
2385 / 3 = 795 (the remainder is 0, so 3 is a divisor of 2385)
...
2385 / 2384 = 1.0004194630872 (the remainder is 1, so 2384 is not a divisor of 2385)
2385 / 2385 = 1 (the remainder is 0, so 2385 is a divisor of 2385)

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 2385 (i.e. 48.836461788299). 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 $\frac{N}{d} = D$ )

2385 / 1 = 2385 (the remainder is 0, so 1 and 2385 are divisors of 2385)
2385 / 2 = 1192.5 (the remainder is 1, so 2 is not a divisor of 2385)
2385 / 3 = 795 (the remainder is 0, so 3 and 795 are divisors of 2385)
...
2385 / 47 = 50.744680851064 (the remainder is 35, so 47 is not a divisor of 2385)
2385 / 48 = 49.6875 (the remainder is 33, so 48 is not a divisor of 2385)