What are the divisors of 592?

1, 2, 4, 8, 16, 37, 74, 148, 296, 592

There is a total of 10 positive divisors.
The sum of these divisors is 1178.
The arithmetic mean is 117.8.

8 even divisors

2, 4, 8, 16, 74, 148, 296, 592

2 odd divisors

1, 37

How to compute the divisors of 592?

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 592 by each of the numbers from 1 to 592 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)

592 / 1 = 592 (the remainder is 0, so 1 is a divisor of 592)
592 / 2 = 296 (the remainder is 0, so 2 is a divisor of 592)
592 / 3 = 197.33333333333 (the remainder is 1, so 3 is not a divisor of 592)
...
592 / 591 = 1.0016920473773 (the remainder is 1, so 591 is not a divisor of 592)
592 / 592 = 1 (the remainder is 0, so 592 is a divisor of 592)

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 592 (i.e. 24.331050121193). 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 $\frac{N}{d} = D$ )

592 / 1 = 592 (the remainder is 0, so 1 and 592 are divisors of 592)
592 / 2 = 296 (the remainder is 0, so 2 and 296 are divisors of 592)
592 / 3 = 197.33333333333 (the remainder is 1, so 3 is not a divisor of 592)
...
592 / 23 = 25.739130434783 (the remainder is 17, so 23 is not a divisor of 592)
592 / 24 = 24.666666666667 (the remainder is 16, so 24 is not a divisor of 592)