What are the divisors of 1812?

1, 2, 3, 4, 6, 12, 151, 302, 453, 604, 906, 1812

There is a total of 12 positive divisors.
The sum of these divisors is 4256.
The arithmetic mean is 354.66666666667.

8 even divisors

2, 4, 6, 12, 302, 604, 906, 1812

4 odd divisors

1, 3, 151, 453

How to compute the divisors of 1812?

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 1812 by each of the numbers from 1 to 1812 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)

1812 / 1 = 1812 (the remainder is 0, so 1 is a divisor of 1812)
1812 / 2 = 906 (the remainder is 0, so 2 is a divisor of 1812)
1812 / 3 = 604 (the remainder is 0, so 3 is a divisor of 1812)
...
1812 / 1811 = 1.0005521811154 (the remainder is 1, so 1811 is not a divisor of 1812)
1812 / 1812 = 1 (the remainder is 0, so 1812 is a divisor of 1812)

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 1812 (i.e. 42.567593307586). 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 $\frac{N}{d} = D$ )

1812 / 1 = 1812 (the remainder is 0, so 1 and 1812 are divisors of 1812)
1812 / 2 = 906 (the remainder is 0, so 2 and 906 are divisors of 1812)
1812 / 3 = 604 (the remainder is 0, so 3 and 604 are divisors of 1812)
...
1812 / 41 = 44.19512195122 (the remainder is 8, so 41 is not a divisor of 1812)
1812 / 42 = 43.142857142857 (the remainder is 6, so 42 is not a divisor of 1812)