What are the divisors of 5801?

1, 5801

There is a total of 2 positive divisors.
The sum of these divisors is 5802.
The arithmetic mean is 2901.

2 odd divisors

1, 5801

How to compute the divisors of 5801?

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 5801 by each of the numbers from 1 to 5801 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)

5801 / 1 = 5801 (the remainder is 0, so 1 is a divisor of 5801)
5801 / 2 = 2900.5 (the remainder is 1, so 2 is not a divisor of 5801)
5801 / 3 = 1933.6666666667 (the remainder is 2, so 3 is not a divisor of 5801)
...
5801 / 5800 = 1.0001724137931 (the remainder is 1, so 5800 is not a divisor of 5801)
5801 / 5801 = 1 (the remainder is 0, so 5801 is a divisor of 5801)

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 5801 (i.e. 76.164296097318). 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 $\frac{N}{d} = D$ )

5801 / 1 = 5801 (the remainder is 0, so 1 and 5801 are divisors of 5801)
5801 / 2 = 2900.5 (the remainder is 1, so 2 is not a divisor of 5801)
5801 / 3 = 1933.6666666667 (the remainder is 2, so 3 is not a divisor of 5801)
...
5801 / 75 = 77.346666666667 (the remainder is 26, so 75 is not a divisor of 5801)
5801 / 76 = 76.328947368421 (the remainder is 25, so 76 is not a divisor of 5801)