What are the divisors of 5792?

1, 2, 4, 8, 16, 32, 181, 362, 724, 1448, 2896, 5792

There is a total of 12 positive divisors.
The sum of these divisors is 11466.
The arithmetic mean is 955.5.

10 even divisors

2, 4, 8, 16, 32, 362, 724, 1448, 2896, 5792

2 odd divisors

1, 181

How to compute the divisors of 5792?

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 5792 by each of the numbers from 1 to 5792 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)

5792 / 1 = 5792 (the remainder is 0, so 1 is a divisor of 5792)
5792 / 2 = 2896 (the remainder is 0, so 2 is a divisor of 5792)
5792 / 3 = 1930.6666666667 (the remainder is 2, so 3 is not a divisor of 5792)
...
5792 / 5791 = 1.0001726817475 (the remainder is 1, so 5791 is not a divisor of 5792)
5792 / 5792 = 1 (the remainder is 0, so 5792 is a divisor of 5792)

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 5792 (i.e. 76.105190361762). 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 $\frac{N}{d} = D$ )

5792 / 1 = 5792 (the remainder is 0, so 1 and 5792 are divisors of 5792)
5792 / 2 = 2896 (the remainder is 0, so 2 and 2896 are divisors of 5792)
5792 / 3 = 1930.6666666667 (the remainder is 2, so 3 is not a divisor of 5792)
...
5792 / 75 = 77.226666666667 (the remainder is 17, so 75 is not a divisor of 5792)
5792 / 76 = 76.210526315789 (the remainder is 16, so 76 is not a divisor of 5792)