What are the divisors of 7059?

1, 3, 13, 39, 181, 543, 2353, 7059

There is a total of 8 positive divisors.
The sum of these divisors is 10192.
The arithmetic mean is 1274.

8 odd divisors

1, 3, 13, 39, 181, 543, 2353, 7059

How to compute the divisors of 7059?

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 7059 by each of the numbers from 1 to 7059 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)

7059 / 1 = 7059 (the remainder is 0, so 1 is a divisor of 7059)
7059 / 2 = 3529.5 (the remainder is 1, so 2 is not a divisor of 7059)
7059 / 3 = 2353 (the remainder is 0, so 3 is a divisor of 7059)
...
7059 / 7058 = 1.0001416831964 (the remainder is 1, so 7058 is not a divisor of 7059)
7059 / 7059 = 1 (the remainder is 0, so 7059 is a divisor of 7059)

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 7059 (i.e. 84.01785524518). 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 $\frac{N}{d} = D$ )

7059 / 1 = 7059 (the remainder is 0, so 1 and 7059 are divisors of 7059)
7059 / 2 = 3529.5 (the remainder is 1, so 2 is not a divisor of 7059)
7059 / 3 = 2353 (the remainder is 0, so 3 and 2353 are divisors of 7059)
...
7059 / 83 = 85.048192771084 (the remainder is 4, so 83 is not a divisor of 7059)
7059 / 84 = 84.035714285714 (the remainder is 3, so 84 is not a divisor of 7059)