What are the divisors of 2822?

1, 2, 17, 34, 83, 166, 1411, 2822

There is a total of 8 positive divisors.
The sum of these divisors is 4536.
The arithmetic mean is 567.

4 even divisors

2, 34, 166, 2822

4 odd divisors

1, 17, 83, 1411

How to compute the divisors of 2822?

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 2822 by each of the numbers from 1 to 2822 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)

2822 / 1 = 2822 (the remainder is 0, so 1 is a divisor of 2822)
2822 / 2 = 1411 (the remainder is 0, so 2 is a divisor of 2822)
2822 / 3 = 940.66666666667 (the remainder is 2, so 3 is not a divisor of 2822)
...
2822 / 2821 = 1.0003544842255 (the remainder is 1, so 2821 is not a divisor of 2822)
2822 / 2822 = 1 (the remainder is 0, so 2822 is a divisor of 2822)

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 2822 (i.e. 53.122499941174). 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 $\frac{N}{d} = D$ )

2822 / 1 = 2822 (the remainder is 0, so 1 and 2822 are divisors of 2822)
2822 / 2 = 1411 (the remainder is 0, so 2 and 1411 are divisors of 2822)
2822 / 3 = 940.66666666667 (the remainder is 2, so 3 is not a divisor of 2822)
...
2822 / 52 = 54.269230769231 (the remainder is 14, so 52 is not a divisor of 2822)
2822 / 53 = 53.245283018868 (the remainder is 13, so 53 is not a divisor of 2822)