What are the divisors of 5783?

1, 5783

There is a total of 2 positive divisors.
The sum of these divisors is 5784.
The arithmetic mean is 2892.

2 odd divisors

1, 5783

How to compute the divisors of 5783?

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 5783 by each of the numbers from 1 to 5783 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)

5783 / 1 = 5783 (the remainder is 0, so 1 is a divisor of 5783)
5783 / 2 = 2891.5 (the remainder is 1, so 2 is not a divisor of 5783)
5783 / 3 = 1927.6666666667 (the remainder is 2, so 3 is not a divisor of 5783)
...
5783 / 5782 = 1.0001729505361 (the remainder is 1, so 5782 is not a divisor of 5783)
5783 / 5783 = 1 (the remainder is 0, so 5783 is a divisor of 5783)

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 5783 (i.e. 76.046038687101). 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 $\frac{N}{d} = D$ )

5783 / 1 = 5783 (the remainder is 0, so 1 and 5783 are divisors of 5783)
5783 / 2 = 2891.5 (the remainder is 1, so 2 is not a divisor of 5783)
5783 / 3 = 1927.6666666667 (the remainder is 2, so 3 is not a divisor of 5783)
...
5783 / 75 = 77.106666666667 (the remainder is 8, so 75 is not a divisor of 5783)
5783 / 76 = 76.092105263158 (the remainder is 7, so 76 is not a divisor of 5783)