What are the divisors of 2684?

1, 2, 4, 11, 22, 44, 61, 122, 244, 671, 1342, 2684

There is a total of 12 positive divisors.
The sum of these divisors is 5208.
The arithmetic mean is 434.

8 even divisors

2, 4, 22, 44, 122, 244, 1342, 2684

4 odd divisors

1, 11, 61, 671

How to compute the divisors of 2684?

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 2684 by each of the numbers from 1 to 2684 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)

2684 / 1 = 2684 (the remainder is 0, so 1 is a divisor of 2684)
2684 / 2 = 1342 (the remainder is 0, so 2 is a divisor of 2684)
2684 / 3 = 894.66666666667 (the remainder is 2, so 3 is not a divisor of 2684)
...
2684 / 2683 = 1.0003727171077 (the remainder is 1, so 2683 is not a divisor of 2684)
2684 / 2684 = 1 (the remainder is 0, so 2684 is a divisor of 2684)

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 2684 (i.e. 51.807335387954). 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 $\frac{N}{d} = D$ )

2684 / 1 = 2684 (the remainder is 0, so 1 and 2684 are divisors of 2684)
2684 / 2 = 1342 (the remainder is 0, so 2 and 1342 are divisors of 2684)
2684 / 3 = 894.66666666667 (the remainder is 2, so 3 is not a divisor of 2684)
...
2684 / 50 = 53.68 (the remainder is 34, so 50 is not a divisor of 2684)
2684 / 51 = 52.627450980392 (the remainder is 32, so 51 is not a divisor of 2684)