What are the divisors of 5832?

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, 729, 972, 1458, 1944, 2916, 5832

There is a total of 28 positive divisors.
The sum of these divisors is 16395.
The arithmetic mean is 585.53571428571.

21 even divisors

2, 4, 6, 8, 12, 18, 24, 36, 54, 72, 108, 162, 216, 324, 486, 648, 972, 1458, 1944, 2916, 5832

7 odd divisors

1, 3, 9, 27, 81, 243, 729

How to compute the divisors of 5832?

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 5832 by each of the numbers from 1 to 5832 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)

5832 / 1 = 5832 (the remainder is 0, so 1 is a divisor of 5832)
5832 / 2 = 2916 (the remainder is 0, so 2 is a divisor of 5832)
5832 / 3 = 1944 (the remainder is 0, so 3 is a divisor of 5832)
...
5832 / 5831 = 1.0001714971703 (the remainder is 1, so 5831 is not a divisor of 5832)
5832 / 5832 = 1 (the remainder is 0, so 5832 is a divisor of 5832)

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 5832 (i.e. 76.367532368147). 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 $\frac{N}{d} = D$ )

5832 / 1 = 5832 (the remainder is 0, so 1 and 5832 are divisors of 5832)
5832 / 2 = 2916 (the remainder is 0, so 2 and 2916 are divisors of 5832)
5832 / 3 = 1944 (the remainder is 0, so 3 and 1944 are divisors of 5832)
...
5832 / 75 = 77.76 (the remainder is 57, so 75 is not a divisor of 5832)
5832 / 76 = 76.736842105263 (the remainder is 56, so 76 is not a divisor of 5832)