What are the divisors of 935?

1, 5, 11, 17, 55, 85, 187, 935

There is a total of 8 positive divisors.
The sum of these divisors is 1296.
The arithmetic mean is 162.

8 odd divisors

1, 5, 11, 17, 55, 85, 187, 935

How to compute the divisors of 935?

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 935 by each of the numbers from 1 to 935 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)

935 / 1 = 935 (the remainder is 0, so 1 is a divisor of 935)
935 / 2 = 467.5 (the remainder is 1, so 2 is not a divisor of 935)
935 / 3 = 311.66666666667 (the remainder is 2, so 3 is not a divisor of 935)
...
935 / 934 = 1.0010706638116 (the remainder is 1, so 934 is not a divisor of 935)
935 / 935 = 1 (the remainder is 0, so 935 is a divisor of 935)

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 935 (i.e. 30.577769702841). 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 $\frac{N}{d} = D$ )

935 / 1 = 935 (the remainder is 0, so 1 and 935 are divisors of 935)
935 / 2 = 467.5 (the remainder is 1, so 2 is not a divisor of 935)
935 / 3 = 311.66666666667 (the remainder is 2, so 3 is not a divisor of 935)
...
935 / 29 = 32.241379310345 (the remainder is 7, so 29 is not a divisor of 935)
935 / 30 = 31.166666666667 (the remainder is 5, so 30 is not a divisor of 935)