What are the divisors of 288?

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288

There is a total of 18 positive divisors.
The sum of these divisors is 819.
The arithmetic mean is 45.5.

15 even divisors

2, 4, 6, 8, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288

3 odd divisors

1, 3, 9

How to compute the divisors of 288?

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 288 by each of the numbers from 1 to 288 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)

288 / 1 = 288 (the remainder is 0, so 1 is a divisor of 288)
288 / 2 = 144 (the remainder is 0, so 2 is a divisor of 288)
288 / 3 = 96 (the remainder is 0, so 3 is a divisor of 288)
...
288 / 287 = 1.0034843205575 (the remainder is 1, so 287 is not a divisor of 288)
288 / 288 = 1 (the remainder is 0, so 288 is a divisor of 288)

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 288 (i.e. 16.970562748477). 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 $\frac{N}{d} = D$ )

288 / 1 = 288 (the remainder is 0, so 1 and 288 are divisors of 288)
288 / 2 = 144 (the remainder is 0, so 2 and 144 are divisors of 288)
288 / 3 = 96 (the remainder is 0, so 3 and 96 are divisors of 288)
...
288 / 15 = 19.2 (the remainder is 3, so 15 is not a divisor of 288)
288 / 16 = 18 (the remainder is 0, so 16 and 18 are divisors of 288)