What are the divisors of 5713?

1, 29, 197, 5713

There is a total of 4 positive divisors.
The sum of these divisors is 5940.
The arithmetic mean is 1485.

4 odd divisors

1, 29, 197, 5713

How to compute the divisors of 5713?

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 5713 by each of the numbers from 1 to 5713 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)

5713 / 1 = 5713 (the remainder is 0, so 1 is a divisor of 5713)
5713 / 2 = 2856.5 (the remainder is 1, so 2 is not a divisor of 5713)
5713 / 3 = 1904.3333333333 (the remainder is 1, so 3 is not a divisor of 5713)
...
5713 / 5712 = 1.000175070028 (the remainder is 1, so 5712 is not a divisor of 5713)
5713 / 5713 = 1 (the remainder is 0, so 5713 is a divisor of 5713)

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 5713 (i.e. 75.584389922788). 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 $\frac{N}{d} = D$ )

5713 / 1 = 5713 (the remainder is 0, so 1 and 5713 are divisors of 5713)
5713 / 2 = 2856.5 (the remainder is 1, so 2 is not a divisor of 5713)
5713 / 3 = 1904.3333333333 (the remainder is 1, so 3 is not a divisor of 5713)
...
5713 / 74 = 77.202702702703 (the remainder is 15, so 74 is not a divisor of 5713)
5713 / 75 = 76.173333333333 (the remainder is 13, so 75 is not a divisor of 5713)