What are the divisors of 8211?

1, 3, 7, 17, 21, 23, 51, 69, 119, 161, 357, 391, 483, 1173, 2737, 8211

There is a total of 16 positive divisors.
The sum of these divisors is 13824.
The arithmetic mean is 864.

16 odd divisors

1, 3, 7, 17, 21, 23, 51, 69, 119, 161, 357, 391, 483, 1173, 2737, 8211

How to compute the divisors of 8211?

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 8211 by each of the numbers from 1 to 8211 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)

8211 / 1 = 8211 (the remainder is 0, so 1 is a divisor of 8211)
8211 / 2 = 4105.5 (the remainder is 1, so 2 is not a divisor of 8211)
8211 / 3 = 2737 (the remainder is 0, so 3 is a divisor of 8211)
...
8211 / 8210 = 1.0001218026797 (the remainder is 1, so 8210 is not a divisor of 8211)
8211 / 8211 = 1 (the remainder is 0, so 8211 is a divisor of 8211)

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 8211 (i.e. 90.614568365137). 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 $\frac{N}{d} = D$ )

8211 / 1 = 8211 (the remainder is 0, so 1 and 8211 are divisors of 8211)
8211 / 2 = 4105.5 (the remainder is 1, so 2 is not a divisor of 8211)
8211 / 3 = 2737 (the remainder is 0, so 3 and 2737 are divisors of 8211)
...
8211 / 89 = 92.258426966292 (the remainder is 23, so 89 is not a divisor of 8211)
8211 / 90 = 91.233333333333 (the remainder is 21, so 90 is not a divisor of 8211)