What are the divisors of 895?

1, 5, 179, 895

There is a total of 4 positive divisors.
The sum of these divisors is 1080.
The arithmetic mean is 270.

4 odd divisors

1, 5, 179, 895

How to compute the divisors of 895?

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 895 by each of the numbers from 1 to 895 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)

895 / 1 = 895 (the remainder is 0, so 1 is a divisor of 895)
895 / 2 = 447.5 (the remainder is 1, so 2 is not a divisor of 895)
895 / 3 = 298.33333333333 (the remainder is 1, so 3 is not a divisor of 895)
...
895 / 894 = 1.0011185682327 (the remainder is 1, so 894 is not a divisor of 895)
895 / 895 = 1 (the remainder is 0, so 895 is a divisor of 895)

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 895 (i.e. 29.916550603303). 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 $\frac{N}{d} = D$ )

895 / 1 = 895 (the remainder is 0, so 1 and 895 are divisors of 895)
895 / 2 = 447.5 (the remainder is 1, so 2 is not a divisor of 895)
895 / 3 = 298.33333333333 (the remainder is 1, so 3 is not a divisor of 895)
...
895 / 28 = 31.964285714286 (the remainder is 27, so 28 is not a divisor of 895)
895 / 29 = 30.862068965517 (the remainder is 25, so 29 is not a divisor of 895)