What are the divisors of 5821?

1, 5821

There is a total of 2 positive divisors.
The sum of these divisors is 5822.
The arithmetic mean is 2911.

2 odd divisors

1, 5821

How to compute the divisors of 5821?

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 5821 by each of the numbers from 1 to 5821 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)

5821 / 1 = 5821 (the remainder is 0, so 1 is a divisor of 5821)
5821 / 2 = 2910.5 (the remainder is 1, so 2 is not a divisor of 5821)
5821 / 3 = 1940.3333333333 (the remainder is 1, so 3 is not a divisor of 5821)
...
5821 / 5820 = 1.0001718213058 (the remainder is 1, so 5820 is not a divisor of 5821)
5821 / 5821 = 1 (the remainder is 0, so 5821 is a divisor of 5821)

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 5821 (i.e. 76.29547824085). 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 $\frac{N}{d} = D$ )

5821 / 1 = 5821 (the remainder is 0, so 1 and 5821 are divisors of 5821)
5821 / 2 = 2910.5 (the remainder is 1, so 2 is not a divisor of 5821)
5821 / 3 = 1940.3333333333 (the remainder is 1, so 3 is not a divisor of 5821)
...
5821 / 75 = 77.613333333333 (the remainder is 46, so 75 is not a divisor of 5821)
5821 / 76 = 76.592105263158 (the remainder is 45, so 76 is not a divisor of 5821)