What are the divisors of 5719?

1, 7, 19, 43, 133, 301, 817, 5719

There is a total of 8 positive divisors.
The sum of these divisors is 7040.
The arithmetic mean is 880.

8 odd divisors

1, 7, 19, 43, 133, 301, 817, 5719

How to compute the divisors of 5719?

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 5719 by each of the numbers from 1 to 5719 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)

5719 / 1 = 5719 (the remainder is 0, so 1 is a divisor of 5719)
5719 / 2 = 2859.5 (the remainder is 1, so 2 is not a divisor of 5719)
5719 / 3 = 1906.3333333333 (the remainder is 1, so 3 is not a divisor of 5719)
...
5719 / 5718 = 1.0001748863239 (the remainder is 1, so 5718 is not a divisor of 5719)
5719 / 5719 = 1 (the remainder is 0, so 5719 is a divisor of 5719)

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 5719 (i.e. 75.624070242219). 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 $\frac{N}{d} = D$ )

5719 / 1 = 5719 (the remainder is 0, so 1 and 5719 are divisors of 5719)
5719 / 2 = 2859.5 (the remainder is 1, so 2 is not a divisor of 5719)
5719 / 3 = 1906.3333333333 (the remainder is 1, so 3 is not a divisor of 5719)
...
5719 / 74 = 77.283783783784 (the remainder is 21, so 74 is not a divisor of 5719)
5719 / 75 = 76.253333333333 (the remainder is 19, so 75 is not a divisor of 5719)