What are the divisors of 2818?

1, 2, 1409, 2818

There is a total of 4 positive divisors.
The sum of these divisors is 4230.
The arithmetic mean is 1057.5.

2 even divisors

2, 2818

2 odd divisors

1, 1409

How to compute the divisors of 2818?

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 2818 by each of the numbers from 1 to 2818 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)

2818 / 1 = 2818 (the remainder is 0, so 1 is a divisor of 2818)
2818 / 2 = 1409 (the remainder is 0, so 2 is a divisor of 2818)
2818 / 3 = 939.33333333333 (the remainder is 1, so 3 is not a divisor of 2818)
...
2818 / 2817 = 1.0003549875754 (the remainder is 1, so 2817 is not a divisor of 2818)
2818 / 2818 = 1 (the remainder is 0, so 2818 is a divisor of 2818)

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 2818 (i.e. 53.084837759948). 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 $\frac{N}{d} = D$ )

2818 / 1 = 2818 (the remainder is 0, so 1 and 2818 are divisors of 2818)
2818 / 2 = 1409 (the remainder is 0, so 2 and 1409 are divisors of 2818)
2818 / 3 = 939.33333333333 (the remainder is 1, so 3 is not a divisor of 2818)
...
2818 / 52 = 54.192307692308 (the remainder is 10, so 52 is not a divisor of 2818)
2818 / 53 = 53.169811320755 (the remainder is 9, so 53 is not a divisor of 2818)