What are the divisors of 5721?

1, 3, 1907, 5721

There is a total of 4 positive divisors.
The sum of these divisors is 7632.
The arithmetic mean is 1908.

4 odd divisors

1, 3, 1907, 5721

How to compute the divisors of 5721?

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 5721 by each of the numbers from 1 to 5721 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)

5721 / 1 = 5721 (the remainder is 0, so 1 is a divisor of 5721)
5721 / 2 = 2860.5 (the remainder is 1, so 2 is not a divisor of 5721)
5721 / 3 = 1907 (the remainder is 0, so 3 is a divisor of 5721)
...
5721 / 5720 = 1.0001748251748 (the remainder is 1, so 5720 is not a divisor of 5721)
5721 / 5721 = 1 (the remainder is 0, so 5721 is a divisor of 5721)

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 5721 (i.e. 75.637292389403). 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 $\frac{N}{d} = D$ )

5721 / 1 = 5721 (the remainder is 0, so 1 and 5721 are divisors of 5721)
5721 / 2 = 2860.5 (the remainder is 1, so 2 is not a divisor of 5721)
5721 / 3 = 1907 (the remainder is 0, so 3 and 1907 are divisors of 5721)
...
5721 / 74 = 77.310810810811 (the remainder is 23, so 74 is not a divisor of 5721)
5721 / 75 = 76.28 (the remainder is 21, so 75 is not a divisor of 5721)