What are the divisors of 7011?

1, 3, 9, 19, 41, 57, 123, 171, 369, 779, 2337, 7011

There is a total of 12 positive divisors.
The sum of these divisors is 10920.
The arithmetic mean is 910.

12 odd divisors

1, 3, 9, 19, 41, 57, 123, 171, 369, 779, 2337, 7011

How to compute the divisors of 7011?

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 7011 by each of the numbers from 1 to 7011 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)

7011 / 1 = 7011 (the remainder is 0, so 1 is a divisor of 7011)
7011 / 2 = 3505.5 (the remainder is 1, so 2 is not a divisor of 7011)
7011 / 3 = 2337 (the remainder is 0, so 3 is a divisor of 7011)
...
7011 / 7010 = 1.0001426533524 (the remainder is 1, so 7010 is not a divisor of 7011)
7011 / 7011 = 1 (the remainder is 0, so 7011 is a divisor of 7011)

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 7011 (i.e. 83.731714421717). 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 $\frac{N}{d} = D$ )

7011 / 1 = 7011 (the remainder is 0, so 1 and 7011 are divisors of 7011)
7011 / 2 = 3505.5 (the remainder is 1, so 2 is not a divisor of 7011)
7011 / 3 = 2337 (the remainder is 0, so 3 and 2337 are divisors of 7011)
...
7011 / 82 = 85.5 (the remainder is 41, so 82 is not a divisor of 7011)
7011 / 83 = 84.469879518072 (the remainder is 39, so 83 is not a divisor of 7011)