What are the divisors of 5933?

1, 17, 349, 5933

There is a total of 4 positive divisors.
The sum of these divisors is 6300.
The arithmetic mean is 1575.

4 odd divisors

1, 17, 349, 5933

How to compute the divisors of 5933?

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 5933 by each of the numbers from 1 to 5933 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)

5933 / 1 = 5933 (the remainder is 0, so 1 is a divisor of 5933)
5933 / 2 = 2966.5 (the remainder is 1, so 2 is not a divisor of 5933)
5933 / 3 = 1977.6666666667 (the remainder is 2, so 3 is not a divisor of 5933)
...
5933 / 5932 = 1.0001685772084 (the remainder is 1, so 5932 is not a divisor of 5933)
5933 / 5933 = 1 (the remainder is 0, so 5933 is a divisor of 5933)

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 5933 (i.e. 77.025969646607). 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 $\frac{N}{d} = D$ )

5933 / 1 = 5933 (the remainder is 0, so 1 and 5933 are divisors of 5933)
5933 / 2 = 2966.5 (the remainder is 1, so 2 is not a divisor of 5933)
5933 / 3 = 1977.6666666667 (the remainder is 2, so 3 is not a divisor of 5933)
...
5933 / 76 = 78.065789473684 (the remainder is 5, so 76 is not a divisor of 5933)
5933 / 77 = 77.051948051948 (the remainder is 4, so 77 is not a divisor of 5933)