What are the divisors of 1608?

1, 2, 3, 4, 6, 8, 12, 24, 67, 134, 201, 268, 402, 536, 804, 1608

There is a total of 16 positive divisors.
The sum of these divisors is 4080.
The arithmetic mean is 255.

12 even divisors

2, 4, 6, 8, 12, 24, 134, 268, 402, 536, 804, 1608

4 odd divisors

1, 3, 67, 201

How to compute the divisors of 1608?

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 1608 by each of the numbers from 1 to 1608 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)

1608 / 1 = 1608 (the remainder is 0, so 1 is a divisor of 1608)
1608 / 2 = 804 (the remainder is 0, so 2 is a divisor of 1608)
1608 / 3 = 536 (the remainder is 0, so 3 is a divisor of 1608)
...
1608 / 1607 = 1.0006222775358 (the remainder is 1, so 1607 is not a divisor of 1608)
1608 / 1608 = 1 (the remainder is 0, so 1608 is a divisor of 1608)

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 1608 (i.e. 40.099875311527). 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 $\frac{N}{d} = D$ )

1608 / 1 = 1608 (the remainder is 0, so 1 and 1608 are divisors of 1608)
1608 / 2 = 804 (the remainder is 0, so 2 and 804 are divisors of 1608)
1608 / 3 = 536 (the remainder is 0, so 3 and 536 are divisors of 1608)
...
1608 / 39 = 41.230769230769 (the remainder is 9, so 39 is not a divisor of 1608)
1608 / 40 = 40.2 (the remainder is 8, so 40 is not a divisor of 1608)