What are the divisors of 8271?

1, 3, 9, 919, 2757, 8271

There is a total of 6 positive divisors.
The sum of these divisors is 11960.
The arithmetic mean is 1993.3333333333.

6 odd divisors

1, 3, 9, 919, 2757, 8271

How to compute the divisors of 8271?

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 8271 by each of the numbers from 1 to 8271 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)

8271 / 1 = 8271 (the remainder is 0, so 1 is a divisor of 8271)
8271 / 2 = 4135.5 (the remainder is 1, so 2 is not a divisor of 8271)
8271 / 3 = 2757 (the remainder is 0, so 3 is a divisor of 8271)
...
8271 / 8270 = 1.0001209189843 (the remainder is 1, so 8270 is not a divisor of 8271)
8271 / 8271 = 1 (the remainder is 0, so 8271 is a divisor of 8271)

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 8271 (i.e. 90.945038347345). 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 $\frac{N}{d} = D$ )

8271 / 1 = 8271 (the remainder is 0, so 1 and 8271 are divisors of 8271)
8271 / 2 = 4135.5 (the remainder is 1, so 2 is not a divisor of 8271)
8271 / 3 = 2757 (the remainder is 0, so 3 and 2757 are divisors of 8271)
...
8271 / 89 = 92.932584269663 (the remainder is 83, so 89 is not a divisor of 8271)
8271 / 90 = 91.9 (the remainder is 81, so 90 is not a divisor of 8271)