What are the divisors of 3756?

1, 2, 3, 4, 6, 12, 313, 626, 939, 1252, 1878, 3756

There is a total of 12 positive divisors.
The sum of these divisors is 8792.
The arithmetic mean is 732.66666666667.

8 even divisors

2, 4, 6, 12, 626, 1252, 1878, 3756

4 odd divisors

1, 3, 313, 939

How to compute the divisors of 3756?

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 3756 by each of the numbers from 1 to 3756 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)

3756 / 1 = 3756 (the remainder is 0, so 1 is a divisor of 3756)
3756 / 2 = 1878 (the remainder is 0, so 2 is a divisor of 3756)
3756 / 3 = 1252 (the remainder is 0, so 3 is a divisor of 3756)
...
3756 / 3755 = 1.0002663115846 (the remainder is 1, so 3755 is not a divisor of 3756)
3756 / 3756 = 1 (the remainder is 0, so 3756 is a divisor of 3756)

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 3756 (i.e. 61.286213784178). 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 $\frac{N}{d} = D$ )

3756 / 1 = 3756 (the remainder is 0, so 1 and 3756 are divisors of 3756)
3756 / 2 = 1878 (the remainder is 0, so 2 and 1878 are divisors of 3756)
3756 / 3 = 1252 (the remainder is 0, so 3 and 1252 are divisors of 3756)
...
3756 / 60 = 62.6 (the remainder is 36, so 60 is not a divisor of 3756)
3756 / 61 = 61.573770491803 (the remainder is 35, so 61 is not a divisor of 3756)