What are the divisors of 9119?

1, 11, 829, 9119

There is a total of 4 positive divisors.
The sum of these divisors is 9960.
The arithmetic mean is 2490.

4 odd divisors

1, 11, 829, 9119

How to compute the divisors of 9119?

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 9119 by each of the numbers from 1 to 9119 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)

9119 / 1 = 9119 (the remainder is 0, so 1 is a divisor of 9119)
9119 / 2 = 4559.5 (the remainder is 1, so 2 is not a divisor of 9119)
9119 / 3 = 3039.6666666667 (the remainder is 2, so 3 is not a divisor of 9119)
...
9119 / 9118 = 1.0001096731739 (the remainder is 1, so 9118 is not a divisor of 9119)
9119 / 9119 = 1 (the remainder is 0, so 9119 is a divisor of 9119)

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 9119 (i.e. 95.493455273123). 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 $\frac{N}{d} = D$ )

9119 / 1 = 9119 (the remainder is 0, so 1 and 9119 are divisors of 9119)
9119 / 2 = 4559.5 (the remainder is 1, so 2 is not a divisor of 9119)
9119 / 3 = 3039.6666666667 (the remainder is 2, so 3 is not a divisor of 9119)
...
9119 / 94 = 97.010638297872 (the remainder is 1, so 94 is not a divisor of 9119)
9119 / 95 = 95.989473684211 (the remainder is 94, so 95 is not a divisor of 9119)