What are the divisors of 5893?

1, 71, 83, 5893

There is a total of 4 positive divisors.
The sum of these divisors is 6048.
The arithmetic mean is 1512.

4 odd divisors

1, 71, 83, 5893

How to compute the divisors of 5893?

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 5893 by each of the numbers from 1 to 5893 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)

5893 / 1 = 5893 (the remainder is 0, so 1 is a divisor of 5893)
5893 / 2 = 2946.5 (the remainder is 1, so 2 is not a divisor of 5893)
5893 / 3 = 1964.3333333333 (the remainder is 1, so 3 is not a divisor of 5893)
...
5893 / 5892 = 1.0001697216565 (the remainder is 1, so 5892 is not a divisor of 5893)
5893 / 5893 = 1 (the remainder is 0, so 5893 is a divisor of 5893)

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 5893 (i.e. 76.765877836445). 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 $\frac{N}{d} = D$ )

5893 / 1 = 5893 (the remainder is 0, so 1 and 5893 are divisors of 5893)
5893 / 2 = 2946.5 (the remainder is 1, so 2 is not a divisor of 5893)
5893 / 3 = 1964.3333333333 (the remainder is 1, so 3 is not a divisor of 5893)
...
5893 / 75 = 78.573333333333 (the remainder is 43, so 75 is not a divisor of 5893)
5893 / 76 = 77.539473684211 (the remainder is 41, so 76 is not a divisor of 5893)