What are the divisors of 2068?

1, 2, 4, 11, 22, 44, 47, 94, 188, 517, 1034, 2068

There is a total of 12 positive divisors.
The sum of these divisors is 4032.
The arithmetic mean is 336.

8 even divisors

2, 4, 22, 44, 94, 188, 1034, 2068

4 odd divisors

1, 11, 47, 517

How to compute the divisors of 2068?

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 2068 by each of the numbers from 1 to 2068 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)

2068 / 1 = 2068 (the remainder is 0, so 1 is a divisor of 2068)
2068 / 2 = 1034 (the remainder is 0, so 2 is a divisor of 2068)
2068 / 3 = 689.33333333333 (the remainder is 1, so 3 is not a divisor of 2068)
...
2068 / 2067 = 1.0004837929366 (the remainder is 1, so 2067 is not a divisor of 2068)
2068 / 2068 = 1 (the remainder is 0, so 2068 is a divisor of 2068)

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 2068 (i.e. 45.475268003608). 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 $\frac{N}{d} = D$ )

2068 / 1 = 2068 (the remainder is 0, so 1 and 2068 are divisors of 2068)
2068 / 2 = 1034 (the remainder is 0, so 2 and 1034 are divisors of 2068)
2068 / 3 = 689.33333333333 (the remainder is 1, so 3 is not a divisor of 2068)
...
2068 / 44 = 47 (the remainder is 0, so 44 and 47 are divisors of 2068)
2068 / 45 = 45.955555555556 (the remainder is 43, so 45 is not a divisor of 2068)