What are the divisors of 5920?

1, 2, 4, 5, 8, 10, 16, 20, 32, 37, 40, 74, 80, 148, 160, 185, 296, 370, 592, 740, 1184, 1480, 2960, 5920

There is a total of 24 positive divisors.
The sum of these divisors is 14364.
The arithmetic mean is 598.5.

20 even divisors

2, 4, 8, 10, 16, 20, 32, 40, 74, 80, 148, 160, 296, 370, 592, 740, 1184, 1480, 2960, 5920

4 odd divisors

1, 5, 37, 185

How to compute the divisors of 5920?

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 5920 by each of the numbers from 1 to 5920 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)

5920 / 1 = 5920 (the remainder is 0, so 1 is a divisor of 5920)
5920 / 2 = 2960 (the remainder is 0, so 2 is a divisor of 5920)
5920 / 3 = 1973.3333333333 (the remainder is 1, so 3 is not a divisor of 5920)
...
5920 / 5919 = 1.0001689474573 (the remainder is 1, so 5919 is not a divisor of 5920)
5920 / 5920 = 1 (the remainder is 0, so 5920 is a divisor of 5920)

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 5920 (i.e. 76.941536246685). 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 $\frac{N}{d} = D$ )

5920 / 1 = 5920 (the remainder is 0, so 1 and 5920 are divisors of 5920)
5920 / 2 = 2960 (the remainder is 0, so 2 and 2960 are divisors of 5920)
5920 / 3 = 1973.3333333333 (the remainder is 1, so 3 is not a divisor of 5920)
...
5920 / 75 = 78.933333333333 (the remainder is 70, so 75 is not a divisor of 5920)
5920 / 76 = 77.894736842105 (the remainder is 68, so 76 is not a divisor of 5920)