What are the divisors of 2812?

1, 2, 4, 19, 37, 38, 74, 76, 148, 703, 1406, 2812

There is a total of 12 positive divisors.
The sum of these divisors is 5320.
The arithmetic mean is 443.33333333333.

8 even divisors

2, 4, 38, 74, 76, 148, 1406, 2812

4 odd divisors

1, 19, 37, 703

How to compute the divisors of 2812?

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 2812 by each of the numbers from 1 to 2812 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)

2812 / 1 = 2812 (the remainder is 0, so 1 is a divisor of 2812)
2812 / 2 = 1406 (the remainder is 0, so 2 is a divisor of 2812)
2812 / 3 = 937.33333333333 (the remainder is 1, so 3 is not a divisor of 2812)
...
2812 / 2811 = 1.0003557452864 (the remainder is 1, so 2811 is not a divisor of 2812)
2812 / 2812 = 1 (the remainder is 0, so 2812 is a divisor of 2812)

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 2812 (i.e. 53.028294334251). 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 $\frac{N}{d} = D$ )

2812 / 1 = 2812 (the remainder is 0, so 1 and 2812 are divisors of 2812)
2812 / 2 = 1406 (the remainder is 0, so 2 and 1406 are divisors of 2812)
2812 / 3 = 937.33333333333 (the remainder is 1, so 3 is not a divisor of 2812)
...
2812 / 52 = 54.076923076923 (the remainder is 4, so 52 is not a divisor of 2812)
2812 / 53 = 53.056603773585 (the remainder is 3, so 53 is not a divisor of 2812)