What are the divisors of 5820?

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 97, 194, 291, 388, 485, 582, 970, 1164, 1455, 1940, 2910, 5820

There is a total of 24 positive divisors.
The sum of these divisors is 16464.
The arithmetic mean is 686.

16 even divisors

2, 4, 6, 10, 12, 20, 30, 60, 194, 388, 582, 970, 1164, 1940, 2910, 5820

8 odd divisors

1, 3, 5, 15, 97, 291, 485, 1455

How to compute the divisors of 5820?

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 5820 by each of the numbers from 1 to 5820 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)

5820 / 1 = 5820 (the remainder is 0, so 1 is a divisor of 5820)
5820 / 2 = 2910 (the remainder is 0, so 2 is a divisor of 5820)
5820 / 3 = 1940 (the remainder is 0, so 3 is a divisor of 5820)
...
5820 / 5819 = 1.0001718508335 (the remainder is 1, so 5819 is not a divisor of 5820)
5820 / 5820 = 1 (the remainder is 0, so 5820 is a divisor of 5820)

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 5820 (i.e. 76.288924491043). 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 $\frac{N}{d} = D$ )

5820 / 1 = 5820 (the remainder is 0, so 1 and 5820 are divisors of 5820)
5820 / 2 = 2910 (the remainder is 0, so 2 and 2910 are divisors of 5820)
5820 / 3 = 1940 (the remainder is 0, so 3 and 1940 are divisors of 5820)
...
5820 / 75 = 77.6 (the remainder is 45, so 75 is not a divisor of 5820)
5820 / 76 = 76.578947368421 (the remainder is 44, so 76 is not a divisor of 5820)