What are the divisors of 5091?

1, 3, 1697, 5091

There is a total of 4 positive divisors.
The sum of these divisors is 6792.
The arithmetic mean is 1698.

4 odd divisors

1, 3, 1697, 5091

How to compute the divisors of 5091?

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 5091 by each of the numbers from 1 to 5091 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)

5091 / 1 = 5091 (the remainder is 0, so 1 is a divisor of 5091)
5091 / 2 = 2545.5 (the remainder is 1, so 2 is not a divisor of 5091)
5091 / 3 = 1697 (the remainder is 0, so 3 is a divisor of 5091)
...
5091 / 5090 = 1.0001964636542 (the remainder is 1, so 5090 is not a divisor of 5091)
5091 / 5091 = 1 (the remainder is 0, so 5091 is a divisor of 5091)

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 5091 (i.e. 71.351243857413). 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 $\frac{N}{d} = D$ )

5091 / 1 = 5091 (the remainder is 0, so 1 and 5091 are divisors of 5091)
5091 / 2 = 2545.5 (the remainder is 1, so 2 is not a divisor of 5091)
5091 / 3 = 1697 (the remainder is 0, so 3 and 1697 are divisors of 5091)
...
5091 / 70 = 72.728571428571 (the remainder is 51, so 70 is not a divisor of 5091)
5091 / 71 = 71.704225352113 (the remainder is 50, so 71 is not a divisor of 5091)