What are the divisors of 3708?

1, 2, 3, 4, 6, 9, 12, 18, 36, 103, 206, 309, 412, 618, 927, 1236, 1854, 3708

There is a total of 18 positive divisors.
The sum of these divisors is 9464.
The arithmetic mean is 525.77777777778.

12 even divisors

2, 4, 6, 12, 18, 36, 206, 412, 618, 1236, 1854, 3708

6 odd divisors

1, 3, 9, 103, 309, 927

How to compute the divisors of 3708?

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 3708 by each of the numbers from 1 to 3708 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)

3708 / 1 = 3708 (the remainder is 0, so 1 is a divisor of 3708)
3708 / 2 = 1854 (the remainder is 0, so 2 is a divisor of 3708)
3708 / 3 = 1236 (the remainder is 0, so 3 is a divisor of 3708)
...
3708 / 3707 = 1.0002697599137 (the remainder is 1, so 3707 is not a divisor of 3708)
3708 / 3708 = 1 (the remainder is 0, so 3708 is a divisor of 3708)

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 3708 (i.e. 60.893349390553). 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 $\frac{N}{d} = D$ )

3708 / 1 = 3708 (the remainder is 0, so 1 and 3708 are divisors of 3708)
3708 / 2 = 1854 (the remainder is 0, so 2 and 1854 are divisors of 3708)
3708 / 3 = 1236 (the remainder is 0, so 3 and 1236 are divisors of 3708)
...
3708 / 59 = 62.847457627119 (the remainder is 50, so 59 is not a divisor of 3708)
3708 / 60 = 61.8 (the remainder is 48, so 60 is not a divisor of 3708)