What are the divisors of 3156?

1, 2, 3, 4, 6, 12, 263, 526, 789, 1052, 1578, 3156

There is a total of 12 positive divisors.
The sum of these divisors is 7392.
The arithmetic mean is 616.

8 even divisors

2, 4, 6, 12, 526, 1052, 1578, 3156

4 odd divisors

1, 3, 263, 789

How to compute the divisors of 3156?

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 3156 by each of the numbers from 1 to 3156 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)

3156 / 1 = 3156 (the remainder is 0, so 1 is a divisor of 3156)
3156 / 2 = 1578 (the remainder is 0, so 2 is a divisor of 3156)
3156 / 3 = 1052 (the remainder is 0, so 3 is a divisor of 3156)
...
3156 / 3155 = 1.0003169572108 (the remainder is 1, so 3155 is not a divisor of 3156)
3156 / 3156 = 1 (the remainder is 0, so 3156 is a divisor of 3156)

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 3156 (i.e. 56.178287620753). 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 $\frac{N}{d} = D$ )

3156 / 1 = 3156 (the remainder is 0, so 1 and 3156 are divisors of 3156)
3156 / 2 = 1578 (the remainder is 0, so 2 and 1578 are divisors of 3156)
3156 / 3 = 1052 (the remainder is 0, so 3 and 1052 are divisors of 3156)
...
3156 / 55 = 57.381818181818 (the remainder is 21, so 55 is not a divisor of 3156)
3156 / 56 = 56.357142857143 (the remainder is 20, so 56 is not a divisor of 3156)