What are the divisors of 8183?

1, 7, 49, 167, 1169, 8183

There is a total of 6 positive divisors.
The sum of these divisors is 9576.
The arithmetic mean is 1596.

6 odd divisors

1, 7, 49, 167, 1169, 8183

How to compute the divisors of 8183?

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 8183 by each of the numbers from 1 to 8183 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)

8183 / 1 = 8183 (the remainder is 0, so 1 is a divisor of 8183)
8183 / 2 = 4091.5 (the remainder is 1, so 2 is not a divisor of 8183)
8183 / 3 = 2727.6666666667 (the remainder is 2, so 3 is not a divisor of 8183)
...
8183 / 8182 = 1.0001222195062 (the remainder is 1, so 8182 is not a divisor of 8183)
8183 / 8183 = 1 (the remainder is 0, so 8183 is a divisor of 8183)

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 8183 (i.e. 90.459935883241). 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 $\frac{N}{d} = D$ )

8183 / 1 = 8183 (the remainder is 0, so 1 and 8183 are divisors of 8183)
8183 / 2 = 4091.5 (the remainder is 1, so 2 is not a divisor of 8183)
8183 / 3 = 2727.6666666667 (the remainder is 2, so 3 is not a divisor of 8183)
...
8183 / 89 = 91.943820224719 (the remainder is 84, so 89 is not a divisor of 8183)
8183 / 90 = 90.922222222222 (the remainder is 83, so 90 is not a divisor of 8183)