What are the divisors of 3706?

1, 2, 17, 34, 109, 218, 1853, 3706

There is a total of 8 positive divisors.
The sum of these divisors is 5940.
The arithmetic mean is 742.5.

4 even divisors

2, 34, 218, 3706

4 odd divisors

1, 17, 109, 1853

How to compute the divisors of 3706?

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 3706 by each of the numbers from 1 to 3706 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)

3706 / 1 = 3706 (the remainder is 0, so 1 is a divisor of 3706)
3706 / 2 = 1853 (the remainder is 0, so 2 is a divisor of 3706)
3706 / 3 = 1235.3333333333 (the remainder is 1, so 3 is not a divisor of 3706)
...
3706 / 3705 = 1.0002699055331 (the remainder is 1, so 3705 is not a divisor of 3706)
3706 / 3706 = 1 (the remainder is 0, so 3706 is a divisor of 3706)

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 3706 (i.e. 60.876925020898). 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 $\frac{N}{d} = D$ )

3706 / 1 = 3706 (the remainder is 0, so 1 and 3706 are divisors of 3706)
3706 / 2 = 1853 (the remainder is 0, so 2 and 1853 are divisors of 3706)
3706 / 3 = 1235.3333333333 (the remainder is 1, so 3 is not a divisor of 3706)
...
3706 / 59 = 62.813559322034 (the remainder is 48, so 59 is not a divisor of 3706)
3706 / 60 = 61.766666666667 (the remainder is 46, so 60 is not a divisor of 3706)