What are the divisors of 5851?

1, 5851

There is a total of 2 positive divisors.
The sum of these divisors is 5852.
The arithmetic mean is 2926.

2 odd divisors

1, 5851

How to compute the divisors of 5851?

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 5851 by each of the numbers from 1 to 5851 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)

5851 / 1 = 5851 (the remainder is 0, so 1 is a divisor of 5851)
5851 / 2 = 2925.5 (the remainder is 1, so 2 is not a divisor of 5851)
5851 / 3 = 1950.3333333333 (the remainder is 1, so 3 is not a divisor of 5851)
...
5851 / 5850 = 1.0001709401709 (the remainder is 1, so 5850 is not a divisor of 5851)
5851 / 5851 = 1 (the remainder is 0, so 5851 is a divisor of 5851)

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 5851 (i.e. 76.491829629053). 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 $\frac{N}{d} = D$ )

5851 / 1 = 5851 (the remainder is 0, so 1 and 5851 are divisors of 5851)
5851 / 2 = 2925.5 (the remainder is 1, so 2 is not a divisor of 5851)
5851 / 3 = 1950.3333333333 (the remainder is 1, so 3 is not a divisor of 5851)
...
5851 / 75 = 78.013333333333 (the remainder is 1, so 75 is not a divisor of 5851)
5851 / 76 = 76.986842105263 (the remainder is 75, so 76 is not a divisor of 5851)