What are the divisors of 6068?

1, 2, 4, 37, 41, 74, 82, 148, 164, 1517, 3034, 6068

There is a total of 12 positive divisors.
The sum of these divisors is 11172.
The arithmetic mean is 931.

8 even divisors

2, 4, 74, 82, 148, 164, 3034, 6068

4 odd divisors

1, 37, 41, 1517

How to compute the divisors of 6068?

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 6068 by each of the numbers from 1 to 6068 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)

6068 / 1 = 6068 (the remainder is 0, so 1 is a divisor of 6068)
6068 / 2 = 3034 (the remainder is 0, so 2 is a divisor of 6068)
6068 / 3 = 2022.6666666667 (the remainder is 2, so 3 is not a divisor of 6068)
...
6068 / 6067 = 1.0001648261085 (the remainder is 1, so 6067 is not a divisor of 6068)
6068 / 6068 = 1 (the remainder is 0, so 6068 is a divisor of 6068)

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 6068 (i.e. 77.897368376602). 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 $\frac{N}{d} = D$ )

6068 / 1 = 6068 (the remainder is 0, so 1 and 6068 are divisors of 6068)
6068 / 2 = 3034 (the remainder is 0, so 2 and 3034 are divisors of 6068)
6068 / 3 = 2022.6666666667 (the remainder is 2, so 3 is not a divisor of 6068)
...
6068 / 76 = 79.842105263158 (the remainder is 64, so 76 is not a divisor of 6068)
6068 / 77 = 78.805194805195 (the remainder is 62, so 77 is not a divisor of 6068)