What are the divisors of 3068?

1, 2, 4, 13, 26, 52, 59, 118, 236, 767, 1534, 3068

There is a total of 12 positive divisors.
The sum of these divisors is 5880.
The arithmetic mean is 490.

8 even divisors

2, 4, 26, 52, 118, 236, 1534, 3068

4 odd divisors

1, 13, 59, 767

How to compute the divisors of 3068?

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 3068 by each of the numbers from 1 to 3068 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)

3068 / 1 = 3068 (the remainder is 0, so 1 is a divisor of 3068)
3068 / 2 = 1534 (the remainder is 0, so 2 is a divisor of 3068)
3068 / 3 = 1022.6666666667 (the remainder is 2, so 3 is not a divisor of 3068)
...
3068 / 3067 = 1.0003260515161 (the remainder is 1, so 3067 is not a divisor of 3068)
3068 / 3068 = 1 (the remainder is 0, so 3068 is a divisor of 3068)

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 3068 (i.e. 55.389529696505). 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 $\frac{N}{d} = D$ )

3068 / 1 = 3068 (the remainder is 0, so 1 and 3068 are divisors of 3068)
3068 / 2 = 1534 (the remainder is 0, so 2 and 1534 are divisors of 3068)
3068 / 3 = 1022.6666666667 (the remainder is 2, so 3 is not a divisor of 3068)
...
3068 / 54 = 56.814814814815 (the remainder is 44, so 54 is not a divisor of 3068)
3068 / 55 = 55.781818181818 (the remainder is 43, so 55 is not a divisor of 3068)