What are the divisors of 885?

1, 3, 5, 15, 59, 177, 295, 885

There is a total of 8 positive divisors.
The sum of these divisors is 1440.
The arithmetic mean is 180.

8 odd divisors

1, 3, 5, 15, 59, 177, 295, 885

How to compute the divisors of 885?

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 885 by each of the numbers from 1 to 885 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)

885 / 1 = 885 (the remainder is 0, so 1 is a divisor of 885)
885 / 2 = 442.5 (the remainder is 1, so 2 is not a divisor of 885)
885 / 3 = 295 (the remainder is 0, so 3 is a divisor of 885)
...
885 / 884 = 1.0011312217195 (the remainder is 1, so 884 is not a divisor of 885)
885 / 885 = 1 (the remainder is 0, so 885 is a divisor of 885)

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 885 (i.e. 29.748949561287). 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 $\frac{N}{d} = D$ )

885 / 1 = 885 (the remainder is 0, so 1 and 885 are divisors of 885)
885 / 2 = 442.5 (the remainder is 1, so 2 is not a divisor of 885)
885 / 3 = 295 (the remainder is 0, so 3 and 295 are divisors of 885)
...
885 / 28 = 31.607142857143 (the remainder is 17, so 28 is not a divisor of 885)
885 / 29 = 30.51724137931 (the remainder is 15, so 29 is not a divisor of 885)