What are the divisors of 8103?

1, 3, 37, 73, 111, 219, 2701, 8103

There is a total of 8 positive divisors.
The sum of these divisors is 11248.
The arithmetic mean is 1406.

8 odd divisors

1, 3, 37, 73, 111, 219, 2701, 8103

How to compute the divisors of 8103?

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 8103 by each of the numbers from 1 to 8103 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)

8103 / 1 = 8103 (the remainder is 0, so 1 is a divisor of 8103)
8103 / 2 = 4051.5 (the remainder is 1, so 2 is not a divisor of 8103)
8103 / 3 = 2701 (the remainder is 0, so 3 is a divisor of 8103)
...
8103 / 8102 = 1.0001234263145 (the remainder is 1, so 8102 is not a divisor of 8103)
8103 / 8103 = 1 (the remainder is 0, so 8103 is a divisor of 8103)

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 8103 (i.e. 90.016665123742). 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 $\frac{N}{d} = D$ )

8103 / 1 = 8103 (the remainder is 0, so 1 and 8103 are divisors of 8103)
8103 / 2 = 4051.5 (the remainder is 1, so 2 is not a divisor of 8103)
8103 / 3 = 2701 (the remainder is 0, so 3 and 2701 are divisors of 8103)
...
8103 / 89 = 91.044943820225 (the remainder is 4, so 89 is not a divisor of 8103)
8103 / 90 = 90.033333333333 (the remainder is 3, so 90 is not a divisor of 8103)