What are the divisors of 5732?

1, 2, 4, 1433, 2866, 5732

There is a total of 6 positive divisors.
The sum of these divisors is 10038.
The arithmetic mean is 1673.

4 even divisors

2, 4, 2866, 5732

2 odd divisors

1, 1433

How to compute the divisors of 5732?

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 5732 by each of the numbers from 1 to 5732 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)

5732 / 1 = 5732 (the remainder is 0, so 1 is a divisor of 5732)
5732 / 2 = 2866 (the remainder is 0, so 2 is a divisor of 5732)
5732 / 3 = 1910.6666666667 (the remainder is 2, so 3 is not a divisor of 5732)
...
5732 / 5731 = 1.0001744896179 (the remainder is 1, so 5731 is not a divisor of 5732)
5732 / 5732 = 1 (the remainder is 0, so 5732 is a divisor of 5732)

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 5732 (i.e. 75.709972922991). 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 $\frac{N}{d} = D$ )

5732 / 1 = 5732 (the remainder is 0, so 1 and 5732 are divisors of 5732)
5732 / 2 = 2866 (the remainder is 0, so 2 and 2866 are divisors of 5732)
5732 / 3 = 1910.6666666667 (the remainder is 2, so 3 is not a divisor of 5732)
...
5732 / 74 = 77.459459459459 (the remainder is 34, so 74 is not a divisor of 5732)
5732 / 75 = 76.426666666667 (the remainder is 32, so 75 is not a divisor of 5732)