What are the divisors of 3726?

1, 2, 3, 6, 9, 18, 23, 27, 46, 54, 69, 81, 138, 162, 207, 414, 621, 1242, 1863, 3726

There is a total of 20 positive divisors.
The sum of these divisors is 8712.
The arithmetic mean is 435.6.

10 even divisors

2, 6, 18, 46, 54, 138, 162, 414, 1242, 3726

10 odd divisors

1, 3, 9, 23, 27, 69, 81, 207, 621, 1863

How to compute the divisors of 3726?

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 3726 by each of the numbers from 1 to 3726 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)

3726 / 1 = 3726 (the remainder is 0, so 1 is a divisor of 3726)
3726 / 2 = 1863 (the remainder is 0, so 2 is a divisor of 3726)
3726 / 3 = 1242 (the remainder is 0, so 3 is a divisor of 3726)
...
3726 / 3725 = 1.0002684563758 (the remainder is 1, so 3725 is not a divisor of 3726)
3726 / 3726 = 1 (the remainder is 0, so 3726 is a divisor of 3726)

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 3726 (i.e. 61.040969848127). 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 $\frac{N}{d} = D$ )

3726 / 1 = 3726 (the remainder is 0, so 1 and 3726 are divisors of 3726)
3726 / 2 = 1863 (the remainder is 0, so 2 and 1863 are divisors of 3726)
3726 / 3 = 1242 (the remainder is 0, so 3 and 1242 are divisors of 3726)
...
3726 / 60 = 62.1 (the remainder is 6, so 60 is not a divisor of 3726)
3726 / 61 = 61.081967213115 (the remainder is 5, so 61 is not a divisor of 3726)