What are the divisors of 5793?

1, 3, 1931, 5793

There is a total of 4 positive divisors.
The sum of these divisors is 7728.
The arithmetic mean is 1932.

4 odd divisors

1, 3, 1931, 5793

How to compute the divisors of 5793?

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 5793 by each of the numbers from 1 to 5793 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)

5793 / 1 = 5793 (the remainder is 0, so 1 is a divisor of 5793)
5793 / 2 = 2896.5 (the remainder is 1, so 2 is not a divisor of 5793)
5793 / 3 = 1931 (the remainder is 0, so 3 is a divisor of 5793)
...
5793 / 5792 = 1.0001726519337 (the remainder is 1, so 5792 is not a divisor of 5793)
5793 / 5793 = 1 (the remainder is 0, so 5793 is a divisor of 5793)

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 5793 (i.e. 76.111759932352). 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 $\frac{N}{d} = D$ )

5793 / 1 = 5793 (the remainder is 0, so 1 and 5793 are divisors of 5793)
5793 / 2 = 2896.5 (the remainder is 1, so 2 is not a divisor of 5793)
5793 / 3 = 1931 (the remainder is 0, so 3 and 1931 are divisors of 5793)
...
5793 / 75 = 77.24 (the remainder is 18, so 75 is not a divisor of 5793)
5793 / 76 = 76.223684210526 (the remainder is 17, so 76 is not a divisor of 5793)