What are the divisors of 1592?

1, 2, 4, 8, 199, 398, 796, 1592

There is a total of 8 positive divisors.
The sum of these divisors is 3000.
The arithmetic mean is 375.

6 even divisors

2, 4, 8, 398, 796, 1592

2 odd divisors

1, 199

How to compute the divisors of 1592?

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 1592 by each of the numbers from 1 to 1592 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)

1592 / 1 = 1592 (the remainder is 0, so 1 is a divisor of 1592)
1592 / 2 = 796 (the remainder is 0, so 2 is a divisor of 1592)
1592 / 3 = 530.66666666667 (the remainder is 2, so 3 is not a divisor of 1592)
...
1592 / 1591 = 1.0006285355123 (the remainder is 1, so 1591 is not a divisor of 1592)
1592 / 1592 = 1 (the remainder is 0, so 1592 is a divisor of 1592)

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 1592 (i.e. 39.89987468652). 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 $\frac{N}{d} = D$ )

1592 / 1 = 1592 (the remainder is 0, so 1 and 1592 are divisors of 1592)
1592 / 2 = 796 (the remainder is 0, so 2 and 796 are divisors of 1592)
1592 / 3 = 530.66666666667 (the remainder is 2, so 3 is not a divisor of 1592)
...
1592 / 38 = 41.894736842105 (the remainder is 34, so 38 is not a divisor of 1592)
1592 / 39 = 40.820512820513 (the remainder is 32, so 39 is not a divisor of 1592)