What are the divisors of 5924?

1, 2, 4, 1481, 2962, 5924

There is a total of 6 positive divisors.
The sum of these divisors is 10374.
The arithmetic mean is 1729.

4 even divisors

2, 4, 2962, 5924

2 odd divisors

1, 1481

How to compute the divisors of 5924?

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 5924 by each of the numbers from 1 to 5924 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)

5924 / 1 = 5924 (the remainder is 0, so 1 is a divisor of 5924)
5924 / 2 = 2962 (the remainder is 0, so 2 is a divisor of 5924)
5924 / 3 = 1974.6666666667 (the remainder is 2, so 3 is not a divisor of 5924)
...
5924 / 5923 = 1.0001688333615 (the remainder is 1, so 5923 is not a divisor of 5924)
5924 / 5924 = 1 (the remainder is 0, so 5924 is a divisor of 5924)

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 5924 (i.e. 76.967525619575). 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 $\frac{N}{d} = D$ )

5924 / 1 = 5924 (the remainder is 0, so 1 and 5924 are divisors of 5924)
5924 / 2 = 2962 (the remainder is 0, so 2 and 2962 are divisors of 5924)
5924 / 3 = 1974.6666666667 (the remainder is 2, so 3 is not a divisor of 5924)
...
5924 / 75 = 78.986666666667 (the remainder is 74, so 75 is not a divisor of 5924)
5924 / 76 = 77.947368421053 (the remainder is 72, so 76 is not a divisor of 5924)