What are the divisors of 384?

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384

There is a total of 16 positive divisors.
The sum of these divisors is 1020.
The arithmetic mean is 63.75.

14 even divisors

2, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384

2 odd divisors

1, 3

How to compute the divisors of 384?

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 384 by each of the numbers from 1 to 384 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)

384 / 1 = 384 (the remainder is 0, so 1 is a divisor of 384)
384 / 2 = 192 (the remainder is 0, so 2 is a divisor of 384)
384 / 3 = 128 (the remainder is 0, so 3 is a divisor of 384)
...
384 / 383 = 1.0026109660574 (the remainder is 1, so 383 is not a divisor of 384)
384 / 384 = 1 (the remainder is 0, so 384 is a divisor of 384)

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 384 (i.e. 19.595917942265). 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 $\frac{N}{d} = D$ )

384 / 1 = 384 (the remainder is 0, so 1 and 384 are divisors of 384)
384 / 2 = 192 (the remainder is 0, so 2 and 192 are divisors of 384)
384 / 3 = 128 (the remainder is 0, so 3 and 128 are divisors of 384)
...
384 / 18 = 21.333333333333 (the remainder is 6, so 18 is not a divisor of 384)
384 / 19 = 20.210526315789 (the remainder is 4, so 19 is not a divisor of 384)