What are the divisors of 7107?

1, 3, 23, 69, 103, 309, 2369, 7107

There is a total of 8 positive divisors.
The sum of these divisors is 9984.
The arithmetic mean is 1248.

8 odd divisors

1, 3, 23, 69, 103, 309, 2369, 7107

How to compute the divisors of 7107?

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 7107 by each of the numbers from 1 to 7107 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)

7107 / 1 = 7107 (the remainder is 0, so 1 is a divisor of 7107)
7107 / 2 = 3553.5 (the remainder is 1, so 2 is not a divisor of 7107)
7107 / 3 = 2369 (the remainder is 0, so 3 is a divisor of 7107)
...
7107 / 7106 = 1.0001407261469 (the remainder is 1, so 7106 is not a divisor of 7107)
7107 / 7107 = 1 (the remainder is 0, so 7107 is a divisor of 7107)

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 7107 (i.e. 84.303024856763). 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 $\frac{N}{d} = D$ )

7107 / 1 = 7107 (the remainder is 0, so 1 and 7107 are divisors of 7107)
7107 / 2 = 3553.5 (the remainder is 1, so 2 is not a divisor of 7107)
7107 / 3 = 2369 (the remainder is 0, so 3 and 2369 are divisors of 7107)
...
7107 / 83 = 85.626506024096 (the remainder is 52, so 83 is not a divisor of 7107)
7107 / 84 = 84.607142857143 (the remainder is 51, so 84 is not a divisor of 7107)