What are the divisors of 7101?

1, 3, 9, 27, 263, 789, 2367, 7101

There is a total of 8 positive divisors.
The sum of these divisors is 10560.
The arithmetic mean is 1320.

8 odd divisors

1, 3, 9, 27, 263, 789, 2367, 7101

How to compute the divisors of 7101?

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 7101 by each of the numbers from 1 to 7101 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)

7101 / 1 = 7101 (the remainder is 0, so 1 is a divisor of 7101)
7101 / 2 = 3550.5 (the remainder is 1, so 2 is not a divisor of 7101)
7101 / 3 = 2367 (the remainder is 0, so 3 is a divisor of 7101)
...
7101 / 7100 = 1.0001408450704 (the remainder is 1, so 7100 is not a divisor of 7101)
7101 / 7101 = 1 (the remainder is 0, so 7101 is a divisor of 7101)

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 7101 (i.e. 84.267431431129). 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 $\frac{N}{d} = D$ )

7101 / 1 = 7101 (the remainder is 0, so 1 and 7101 are divisors of 7101)
7101 / 2 = 3550.5 (the remainder is 1, so 2 is not a divisor of 7101)
7101 / 3 = 2367 (the remainder is 0, so 3 and 2367 are divisors of 7101)
...
7101 / 83 = 85.55421686747 (the remainder is 46, so 83 is not a divisor of 7101)
7101 / 84 = 84.535714285714 (the remainder is 45, so 84 is not a divisor of 7101)