What are the divisors of 1887?

1, 3, 17, 37, 51, 111, 629, 1887

There is a total of 8 positive divisors.
The sum of these divisors is 2736.
The arithmetic mean is 342.

8 odd divisors

1, 3, 17, 37, 51, 111, 629, 1887

How to compute the divisors of 1887?

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 1887 by each of the numbers from 1 to 1887 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)

1887 / 1 = 1887 (the remainder is 0, so 1 is a divisor of 1887)
1887 / 2 = 943.5 (the remainder is 1, so 2 is not a divisor of 1887)
1887 / 3 = 629 (the remainder is 0, so 3 is a divisor of 1887)
...
1887 / 1886 = 1.0005302226935 (the remainder is 1, so 1886 is not a divisor of 1887)
1887 / 1887 = 1 (the remainder is 0, so 1887 is a divisor of 1887)

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 1887 (i.e. 43.439613257947). 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 $\frac{N}{d} = D$ )

1887 / 1 = 1887 (the remainder is 0, so 1 and 1887 are divisors of 1887)
1887 / 2 = 943.5 (the remainder is 1, so 2 is not a divisor of 1887)
1887 / 3 = 629 (the remainder is 0, so 3 and 629 are divisors of 1887)
...
1887 / 42 = 44.928571428571 (the remainder is 39, so 42 is not a divisor of 1887)
1887 / 43 = 43.883720930233 (the remainder is 38, so 43 is not a divisor of 1887)