What are the divisors of 2088?

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 29, 36, 58, 72, 87, 116, 174, 232, 261, 348, 522, 696, 1044, 2088

There is a total of 24 positive divisors.
The sum of these divisors is 5850.
The arithmetic mean is 243.75.

18 even divisors

2, 4, 6, 8, 12, 18, 24, 36, 58, 72, 116, 174, 232, 348, 522, 696, 1044, 2088

6 odd divisors

1, 3, 9, 29, 87, 261

How to compute the divisors of 2088?

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 2088 by each of the numbers from 1 to 2088 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)

2088 / 1 = 2088 (the remainder is 0, so 1 is a divisor of 2088)
2088 / 2 = 1044 (the remainder is 0, so 2 is a divisor of 2088)
2088 / 3 = 696 (the remainder is 0, so 3 is a divisor of 2088)
...
2088 / 2087 = 1.0004791566842 (the remainder is 1, so 2087 is not a divisor of 2088)
2088 / 2088 = 1 (the remainder is 0, so 2088 is a divisor of 2088)

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 2088 (i.e. 45.694638635183). 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 $\frac{N}{d} = D$ )

2088 / 1 = 2088 (the remainder is 0, so 1 and 2088 are divisors of 2088)
2088 / 2 = 1044 (the remainder is 0, so 2 and 1044 are divisors of 2088)
2088 / 3 = 696 (the remainder is 0, so 3 and 696 are divisors of 2088)
...
2088 / 44 = 47.454545454545 (the remainder is 20, so 44 is not a divisor of 2088)
2088 / 45 = 46.4 (the remainder is 18, so 45 is not a divisor of 2088)