What are the divisors of 1885?

1, 5, 13, 29, 65, 145, 377, 1885

There is a total of 8 positive divisors.
The sum of these divisors is 2520.
The arithmetic mean is 315.

8 odd divisors

1, 5, 13, 29, 65, 145, 377, 1885

How to compute the divisors of 1885?

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 1885 by each of the numbers from 1 to 1885 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)

1885 / 1 = 1885 (the remainder is 0, so 1 is a divisor of 1885)
1885 / 2 = 942.5 (the remainder is 1, so 2 is not a divisor of 1885)
1885 / 3 = 628.33333333333 (the remainder is 1, so 3 is not a divisor of 1885)
...
1885 / 1884 = 1.0005307855626 (the remainder is 1, so 1884 is not a divisor of 1885)
1885 / 1885 = 1 (the remainder is 0, so 1885 is a divisor of 1885)

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 1885 (i.e. 43.416586692185). 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 $\frac{N}{d} = D$ )

1885 / 1 = 1885 (the remainder is 0, so 1 and 1885 are divisors of 1885)
1885 / 2 = 942.5 (the remainder is 1, so 2 is not a divisor of 1885)
1885 / 3 = 628.33333333333 (the remainder is 1, so 3 is not a divisor of 1885)
...
1885 / 42 = 44.880952380952 (the remainder is 37, so 42 is not a divisor of 1885)
1885 / 43 = 43.837209302326 (the remainder is 36, so 43 is not a divisor of 1885)