What are the divisors of 3606?

1, 2, 3, 6, 601, 1202, 1803, 3606

There is a total of 8 positive divisors.
The sum of these divisors is 7224.
The arithmetic mean is 903.

4 even divisors

2, 6, 1202, 3606

4 odd divisors

1, 3, 601, 1803

How to compute the divisors of 3606?

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 3606 by each of the numbers from 1 to 3606 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)

3606 / 1 = 3606 (the remainder is 0, so 1 is a divisor of 3606)
3606 / 2 = 1803 (the remainder is 0, so 2 is a divisor of 3606)
3606 / 3 = 1202 (the remainder is 0, so 3 is a divisor of 3606)
...
3606 / 3605 = 1.0002773925104 (the remainder is 1, so 3605 is not a divisor of 3606)
3606 / 3606 = 1 (the remainder is 0, so 3606 is a divisor of 3606)

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 3606 (i.e. 60.04997918401). 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 $\frac{N}{d} = D$ )

3606 / 1 = 3606 (the remainder is 0, so 1 and 3606 are divisors of 3606)
3606 / 2 = 1803 (the remainder is 0, so 2 and 1803 are divisors of 3606)
3606 / 3 = 1202 (the remainder is 0, so 3 and 1202 are divisors of 3606)
...
3606 / 59 = 61.118644067797 (the remainder is 7, so 59 is not a divisor of 3606)
3606 / 60 = 60.1 (the remainder is 6, so 60 is not a divisor of 3606)