What are the divisors of 5794?

1, 2, 2897, 5794

There is a total of 4 positive divisors.
The sum of these divisors is 8694.
The arithmetic mean is 2173.5.

2 even divisors

2, 5794

2 odd divisors

1, 2897

How to compute the divisors of 5794?

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 5794 by each of the numbers from 1 to 5794 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)

5794 / 1 = 5794 (the remainder is 0, so 1 is a divisor of 5794)
5794 / 2 = 2897 (the remainder is 0, so 2 is a divisor of 5794)
5794 / 3 = 1931.3333333333 (the remainder is 1, so 3 is not a divisor of 5794)
...
5794 / 5793 = 1.0001726221302 (the remainder is 1, so 5793 is not a divisor of 5794)
5794 / 5794 = 1 (the remainder is 0, so 5794 is a divisor of 5794)

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 5794 (i.e. 76.11832893594). 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 $\frac{N}{d} = D$ )

5794 / 1 = 5794 (the remainder is 0, so 1 and 5794 are divisors of 5794)
5794 / 2 = 2897 (the remainder is 0, so 2 and 2897 are divisors of 5794)
5794 / 3 = 1931.3333333333 (the remainder is 1, so 3 is not a divisor of 5794)
...
5794 / 75 = 77.253333333333 (the remainder is 19, so 75 is not a divisor of 5794)
5794 / 76 = 76.236842105263 (the remainder is 18, so 76 is not a divisor of 5794)