What are the divisors of 5813?

1, 5813

There is a total of 2 positive divisors.
The sum of these divisors is 5814.
The arithmetic mean is 2907.

2 odd divisors

1, 5813

How to compute the divisors of 5813?

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 5813 by each of the numbers from 1 to 5813 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)

5813 / 1 = 5813 (the remainder is 0, so 1 is a divisor of 5813)
5813 / 2 = 2906.5 (the remainder is 1, so 2 is not a divisor of 5813)
5813 / 3 = 1937.6666666667 (the remainder is 2, so 3 is not a divisor of 5813)
...
5813 / 5812 = 1.0001720578114 (the remainder is 1, so 5812 is not a divisor of 5813)
5813 / 5813 = 1 (the remainder is 0, so 5813 is a divisor of 5813)

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 5813 (i.e. 76.243032468548). 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 $\frac{N}{d} = D$ )

5813 / 1 = 5813 (the remainder is 0, so 1 and 5813 are divisors of 5813)
5813 / 2 = 2906.5 (the remainder is 1, so 2 is not a divisor of 5813)
5813 / 3 = 1937.6666666667 (the remainder is 2, so 3 is not a divisor of 5813)
...
5813 / 75 = 77.506666666667 (the remainder is 38, so 75 is not a divisor of 5813)
5813 / 76 = 76.486842105263 (the remainder is 37, so 76 is not a divisor of 5813)