What are the divisors of 7068?

1, 2, 3, 4, 6, 12, 19, 31, 38, 57, 62, 76, 93, 114, 124, 186, 228, 372, 589, 1178, 1767, 2356, 3534, 7068

There is a total of 24 positive divisors.
The sum of these divisors is 17920.
The arithmetic mean is 746.66666666667.

16 even divisors

2, 4, 6, 12, 38, 62, 76, 114, 124, 186, 228, 372, 1178, 2356, 3534, 7068

8 odd divisors

1, 3, 19, 31, 57, 93, 589, 1767

How to compute the divisors of 7068?

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 7068 by each of the numbers from 1 to 7068 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)

7068 / 1 = 7068 (the remainder is 0, so 1 is a divisor of 7068)
7068 / 2 = 3534 (the remainder is 0, so 2 is a divisor of 7068)
7068 / 3 = 2356 (the remainder is 0, so 3 is a divisor of 7068)
...
7068 / 7067 = 1.0001415027593 (the remainder is 1, so 7067 is not a divisor of 7068)
7068 / 7068 = 1 (the remainder is 0, so 7068 is a divisor of 7068)

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 7068 (i.e. 84.071398227935). 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 $\frac{N}{d} = D$ )

7068 / 1 = 7068 (the remainder is 0, so 1 and 7068 are divisors of 7068)
7068 / 2 = 3534 (the remainder is 0, so 2 and 3534 are divisors of 7068)
7068 / 3 = 2356 (the remainder is 0, so 3 and 2356 are divisors of 7068)
...
7068 / 83 = 85.156626506024 (the remainder is 13, so 83 is not a divisor of 7068)
7068 / 84 = 84.142857142857 (the remainder is 12, so 84 is not a divisor of 7068)