What are the divisors of 9103?

1, 9103

There is a total of 2 positive divisors.
The sum of these divisors is 9104.
The arithmetic mean is 4552.

2 odd divisors

1, 9103

How to compute the divisors of 9103?

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 9103 by each of the numbers from 1 to 9103 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)

9103 / 1 = 9103 (the remainder is 0, so 1 is a divisor of 9103)
9103 / 2 = 4551.5 (the remainder is 1, so 2 is not a divisor of 9103)
9103 / 3 = 3034.3333333333 (the remainder is 1, so 3 is not a divisor of 9103)
...
9103 / 9102 = 1.0001098659635 (the remainder is 1, so 9102 is not a divisor of 9103)
9103 / 9103 = 1 (the remainder is 0, so 9103 is a divisor of 9103)

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 9103 (i.e. 95.409643118502). 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 $\frac{N}{d} = D$ )

9103 / 1 = 9103 (the remainder is 0, so 1 and 9103 are divisors of 9103)
9103 / 2 = 4551.5 (the remainder is 1, so 2 is not a divisor of 9103)
9103 / 3 = 3034.3333333333 (the remainder is 1, so 3 is not a divisor of 9103)
...
9103 / 94 = 96.840425531915 (the remainder is 79, so 94 is not a divisor of 9103)
9103 / 95 = 95.821052631579 (the remainder is 78, so 95 is not a divisor of 9103)