What are the divisors of 1606?

1, 2, 11, 22, 73, 146, 803, 1606

There is a total of 8 positive divisors.
The sum of these divisors is 2664.
The arithmetic mean is 333.

4 even divisors

2, 22, 146, 1606

4 odd divisors

1, 11, 73, 803

How to compute the divisors of 1606?

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 1606 by each of the numbers from 1 to 1606 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)

1606 / 1 = 1606 (the remainder is 0, so 1 is a divisor of 1606)
1606 / 2 = 803 (the remainder is 0, so 2 is a divisor of 1606)
1606 / 3 = 535.33333333333 (the remainder is 1, so 3 is not a divisor of 1606)
...
1606 / 1605 = 1.0006230529595 (the remainder is 1, so 1605 is not a divisor of 1606)
1606 / 1606 = 1 (the remainder is 0, so 1606 is a divisor of 1606)

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 1606 (i.e. 40.074929819028). 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 $\frac{N}{d} = D$ )

1606 / 1 = 1606 (the remainder is 0, so 1 and 1606 are divisors of 1606)
1606 / 2 = 803 (the remainder is 0, so 2 and 803 are divisors of 1606)
1606 / 3 = 535.33333333333 (the remainder is 1, so 3 is not a divisor of 1606)
...
1606 / 39 = 41.179487179487 (the remainder is 7, so 39 is not a divisor of 1606)
1606 / 40 = 40.15 (the remainder is 6, so 40 is not a divisor of 1606)