What are the divisors of 3608?

1, 2, 4, 8, 11, 22, 41, 44, 82, 88, 164, 328, 451, 902, 1804, 3608

There is a total of 16 positive divisors.
The sum of these divisors is 7560.
The arithmetic mean is 472.5.

12 even divisors

2, 4, 8, 22, 44, 82, 88, 164, 328, 902, 1804, 3608

4 odd divisors

1, 11, 41, 451

How to compute the divisors of 3608?

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 3608 by each of the numbers from 1 to 3608 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)

3608 / 1 = 3608 (the remainder is 0, so 1 is a divisor of 3608)
3608 / 2 = 1804 (the remainder is 0, so 2 is a divisor of 3608)
3608 / 3 = 1202.6666666667 (the remainder is 2, so 3 is not a divisor of 3608)
...
3608 / 3607 = 1.0002772387025 (the remainder is 1, so 3607 is not a divisor of 3608)
3608 / 3608 = 1 (the remainder is 0, so 3608 is a divisor of 3608)

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 3608 (i.e. 60.066629670725). 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 $\frac{N}{d} = D$ )

3608 / 1 = 3608 (the remainder is 0, so 1 and 3608 are divisors of 3608)
3608 / 2 = 1804 (the remainder is 0, so 2 and 1804 are divisors of 3608)
3608 / 3 = 1202.6666666667 (the remainder is 2, so 3 is not a divisor of 3608)
...
3608 / 59 = 61.152542372881 (the remainder is 9, so 59 is not a divisor of 3608)
3608 / 60 = 60.133333333333 (the remainder is 8, so 60 is not a divisor of 3608)