What are the divisors of 8169?

1, 3, 7, 21, 389, 1167, 2723, 8169

There is a total of 8 positive divisors.
The sum of these divisors is 12480.
The arithmetic mean is 1560.

8 odd divisors

1, 3, 7, 21, 389, 1167, 2723, 8169

How to compute the divisors of 8169?

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 8169 by each of the numbers from 1 to 8169 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)

8169 / 1 = 8169 (the remainder is 0, so 1 is a divisor of 8169)
8169 / 2 = 4084.5 (the remainder is 1, so 2 is not a divisor of 8169)
8169 / 3 = 2723 (the remainder is 0, so 3 is a divisor of 8169)
...
8169 / 8168 = 1.0001224289912 (the remainder is 1, so 8168 is not a divisor of 8169)
8169 / 8169 = 1 (the remainder is 0, so 8169 is a divisor of 8169)

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 8169 (i.e. 90.382520433987). 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 $\frac{N}{d} = D$ )

8169 / 1 = 8169 (the remainder is 0, so 1 and 8169 are divisors of 8169)
8169 / 2 = 4084.5 (the remainder is 1, so 2 is not a divisor of 8169)
8169 / 3 = 2723 (the remainder is 0, so 3 and 2723 are divisors of 8169)
...
8169 / 89 = 91.786516853933 (the remainder is 70, so 89 is not a divisor of 8169)
8169 / 90 = 90.766666666667 (the remainder is 69, so 90 is not a divisor of 8169)