What are the divisors of 2384?

1, 2, 4, 8, 16, 149, 298, 596, 1192, 2384

There is a total of 10 positive divisors.
The sum of these divisors is 4650.
The arithmetic mean is 465.

8 even divisors

2, 4, 8, 16, 298, 596, 1192, 2384

2 odd divisors

1, 149

How to compute the divisors of 2384?

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 2384 by each of the numbers from 1 to 2384 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)

2384 / 1 = 2384 (the remainder is 0, so 1 is a divisor of 2384)
2384 / 2 = 1192 (the remainder is 0, so 2 is a divisor of 2384)
2384 / 3 = 794.66666666667 (the remainder is 2, so 3 is not a divisor of 2384)
...
2384 / 2383 = 1.0004196391104 (the remainder is 1, so 2383 is not a divisor of 2384)
2384 / 2384 = 1 (the remainder is 0, so 2384 is a divisor of 2384)

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 2384 (i.e. 48.826222462935). 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 $\frac{N}{d} = D$ )

2384 / 1 = 2384 (the remainder is 0, so 1 and 2384 are divisors of 2384)
2384 / 2 = 1192 (the remainder is 0, so 2 and 1192 are divisors of 2384)
2384 / 3 = 794.66666666667 (the remainder is 2, so 3 is not a divisor of 2384)
...
2384 / 47 = 50.723404255319 (the remainder is 34, so 47 is not a divisor of 2384)
2384 / 48 = 49.666666666667 (the remainder is 32, so 48 is not a divisor of 2384)