What are the divisors of 5916?

1, 2, 3, 4, 6, 12, 17, 29, 34, 51, 58, 68, 87, 102, 116, 174, 204, 348, 493, 986, 1479, 1972, 2958, 5916

There is a total of 24 positive divisors.
The sum of these divisors is 15120.
The arithmetic mean is 630.

16 even divisors

2, 4, 6, 12, 34, 58, 68, 102, 116, 174, 204, 348, 986, 1972, 2958, 5916

8 odd divisors

1, 3, 17, 29, 51, 87, 493, 1479

How to compute the divisors of 5916?

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 5916 by each of the numbers from 1 to 5916 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)

5916 / 1 = 5916 (the remainder is 0, so 1 is a divisor of 5916)
5916 / 2 = 2958 (the remainder is 0, so 2 is a divisor of 5916)
5916 / 3 = 1972 (the remainder is 0, so 3 is a divisor of 5916)
...
5916 / 5915 = 1.0001690617075 (the remainder is 1, so 5915 is not a divisor of 5916)
5916 / 5916 = 1 (the remainder is 0, so 5916 is a divisor of 5916)

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 5916 (i.e. 76.915538092118). 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 $\frac{N}{d} = D$ )

5916 / 1 = 5916 (the remainder is 0, so 1 and 5916 are divisors of 5916)
5916 / 2 = 2958 (the remainder is 0, so 2 and 2958 are divisors of 5916)
5916 / 3 = 1972 (the remainder is 0, so 3 and 1972 are divisors of 5916)
...
5916 / 75 = 78.88 (the remainder is 66, so 75 is not a divisor of 5916)
5916 / 76 = 77.842105263158 (the remainder is 64, so 76 is not a divisor of 5916)