What are the divisors of 1236?

1, 2, 3, 4, 6, 12, 103, 206, 309, 412, 618, 1236

There is a total of 12 positive divisors.
The sum of these divisors is 2912.
The arithmetic mean is 242.66666666667.

8 even divisors

2, 4, 6, 12, 206, 412, 618, 1236

4 odd divisors

1, 3, 103, 309

How to compute the divisors of 1236?

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 1236 by each of the numbers from 1 to 1236 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)

1236 / 1 = 1236 (the remainder is 0, so 1 is a divisor of 1236)
1236 / 2 = 618 (the remainder is 0, so 2 is a divisor of 1236)
1236 / 3 = 412 (the remainder is 0, so 3 is a divisor of 1236)
...
1236 / 1235 = 1.0008097165992 (the remainder is 1, so 1235 is not a divisor of 1236)
1236 / 1236 = 1 (the remainder is 0, so 1236 is a divisor of 1236)

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 1236 (i.e. 35.156791662494). 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 $\frac{N}{d} = D$ )

1236 / 1 = 1236 (the remainder is 0, so 1 and 1236 are divisors of 1236)
1236 / 2 = 618 (the remainder is 0, so 2 and 618 are divisors of 1236)
1236 / 3 = 412 (the remainder is 0, so 3 and 412 are divisors of 1236)
...
1236 / 34 = 36.352941176471 (the remainder is 12, so 34 is not a divisor of 1236)
1236 / 35 = 35.314285714286 (the remainder is 11, so 35 is not a divisor of 1236)