What are the divisors of 5722?

1, 2, 2861, 5722

There is a total of 4 positive divisors.
The sum of these divisors is 8586.
The arithmetic mean is 2146.5.

2 even divisors

2, 5722

2 odd divisors

1, 2861

How to compute the divisors of 5722?

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 5722 by each of the numbers from 1 to 5722 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)

5722 / 1 = 5722 (the remainder is 0, so 1 is a divisor of 5722)
5722 / 2 = 2861 (the remainder is 0, so 2 is a divisor of 5722)
5722 / 3 = 1907.3333333333 (the remainder is 1, so 3 is not a divisor of 5722)
...
5722 / 5721 = 1.0001747946163 (the remainder is 1, so 5721 is not a divisor of 5722)
5722 / 5722 = 1 (the remainder is 0, so 5722 is a divisor of 5722)

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 5722 (i.e. 75.64390259631). 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 $\frac{N}{d} = D$ )

5722 / 1 = 5722 (the remainder is 0, so 1 and 5722 are divisors of 5722)
5722 / 2 = 2861 (the remainder is 0, so 2 and 2861 are divisors of 5722)
5722 / 3 = 1907.3333333333 (the remainder is 1, so 3 is not a divisor of 5722)
...
5722 / 74 = 77.324324324324 (the remainder is 24, so 74 is not a divisor of 5722)
5722 / 75 = 76.293333333333 (the remainder is 22, so 75 is not a divisor of 5722)