What are the divisors of 2836?

1, 2, 4, 709, 1418, 2836

There is a total of 6 positive divisors.
The sum of these divisors is 4970.
The arithmetic mean is 828.33333333333.

4 even divisors

2, 4, 1418, 2836

2 odd divisors

1, 709

How to compute the divisors of 2836?

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 2836 by each of the numbers from 1 to 2836 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)

2836 / 1 = 2836 (the remainder is 0, so 1 is a divisor of 2836)
2836 / 2 = 1418 (the remainder is 0, so 2 is a divisor of 2836)
2836 / 3 = 945.33333333333 (the remainder is 1, so 3 is not a divisor of 2836)
...
2836 / 2835 = 1.0003527336861 (the remainder is 1, so 2835 is not a divisor of 2836)
2836 / 2836 = 1 (the remainder is 0, so 2836 is a divisor of 2836)

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 2836 (i.e. 53.254107822777). 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 $\frac{N}{d} = D$ )

2836 / 1 = 2836 (the remainder is 0, so 1 and 2836 are divisors of 2836)
2836 / 2 = 1418 (the remainder is 0, so 2 and 1418 are divisors of 2836)
2836 / 3 = 945.33333333333 (the remainder is 1, so 3 is not a divisor of 2836)
...
2836 / 52 = 54.538461538462 (the remainder is 28, so 52 is not a divisor of 2836)
2836 / 53 = 53.509433962264 (the remainder is 27, so 53 is not a divisor of 2836)