What are the divisors of 1788?

1, 2, 3, 4, 6, 12, 149, 298, 447, 596, 894, 1788

There is a total of 12 positive divisors.
The sum of these divisors is 4200.
The arithmetic mean is 350.

8 even divisors

2, 4, 6, 12, 298, 596, 894, 1788

4 odd divisors

1, 3, 149, 447

How to compute the divisors of 1788?

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 1788 by each of the numbers from 1 to 1788 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)

1788 / 1 = 1788 (the remainder is 0, so 1 is a divisor of 1788)
1788 / 2 = 894 (the remainder is 0, so 2 is a divisor of 1788)
1788 / 3 = 596 (the remainder is 0, so 3 is a divisor of 1788)
...
1788 / 1787 = 1.0005595970901 (the remainder is 1, so 1787 is not a divisor of 1788)
1788 / 1788 = 1 (the remainder is 0, so 1788 is a divisor of 1788)

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 1788 (i.e. 42.284749023732). 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 $\frac{N}{d} = D$ )

1788 / 1 = 1788 (the remainder is 0, so 1 and 1788 are divisors of 1788)
1788 / 2 = 894 (the remainder is 0, so 2 and 894 are divisors of 1788)
1788 / 3 = 596 (the remainder is 0, so 3 and 596 are divisors of 1788)
...
1788 / 41 = 43.609756097561 (the remainder is 25, so 41 is not a divisor of 1788)
1788 / 42 = 42.571428571429 (the remainder is 24, so 42 is not a divisor of 1788)