What are the divisors of 5935?

1, 5, 1187, 5935

There is a total of 4 positive divisors.
The sum of these divisors is 7128.
The arithmetic mean is 1782.

4 odd divisors

1, 5, 1187, 5935

How to compute the divisors of 5935?

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 5935 by each of the numbers from 1 to 5935 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)

5935 / 1 = 5935 (the remainder is 0, so 1 is a divisor of 5935)
5935 / 2 = 2967.5 (the remainder is 1, so 2 is not a divisor of 5935)
5935 / 3 = 1978.3333333333 (the remainder is 1, so 3 is not a divisor of 5935)
...
5935 / 5934 = 1.000168520391 (the remainder is 1, so 5934 is not a divisor of 5935)
5935 / 5935 = 1 (the remainder is 0, so 5935 is a divisor of 5935)

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 5935 (i.e. 77.038951187046). 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 $\frac{N}{d} = D$ )

5935 / 1 = 5935 (the remainder is 0, so 1 and 5935 are divisors of 5935)
5935 / 2 = 2967.5 (the remainder is 1, so 2 is not a divisor of 5935)
5935 / 3 = 1978.3333333333 (the remainder is 1, so 3 is not a divisor of 5935)
...
5935 / 76 = 78.092105263158 (the remainder is 7, so 76 is not a divisor of 5935)
5935 / 77 = 77.077922077922 (the remainder is 6, so 77 is not a divisor of 5935)