What are the divisors of 7029?

1, 3, 9, 11, 33, 71, 99, 213, 639, 781, 2343, 7029

There is a total of 12 positive divisors.
The sum of these divisors is 11232.
The arithmetic mean is 936.

12 odd divisors

1, 3, 9, 11, 33, 71, 99, 213, 639, 781, 2343, 7029

How to compute the divisors of 7029?

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 7029 by each of the numbers from 1 to 7029 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)

7029 / 1 = 7029 (the remainder is 0, so 1 is a divisor of 7029)
7029 / 2 = 3514.5 (the remainder is 1, so 2 is not a divisor of 7029)
7029 / 3 = 2343 (the remainder is 0, so 3 is a divisor of 7029)
...
7029 / 7028 = 1.0001422879909 (the remainder is 1, so 7028 is not a divisor of 7029)
7029 / 7029 = 1 (the remainder is 0, so 7029 is a divisor of 7029)

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 7029 (i.e. 83.839131674893). 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 $\frac{N}{d} = D$ )

7029 / 1 = 7029 (the remainder is 0, so 1 and 7029 are divisors of 7029)
7029 / 2 = 3514.5 (the remainder is 1, so 2 is not a divisor of 7029)
7029 / 3 = 2343 (the remainder is 0, so 3 and 2343 are divisors of 7029)
...
7029 / 82 = 85.719512195122 (the remainder is 59, so 82 is not a divisor of 7029)
7029 / 83 = 84.686746987952 (the remainder is 57, so 83 is not a divisor of 7029)