What are the divisors of 9019?

1, 29, 311, 9019

There is a total of 4 positive divisors.
The sum of these divisors is 9360.
The arithmetic mean is 2340.

4 odd divisors

1, 29, 311, 9019

How to compute the divisors of 9019?

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 9019 by each of the numbers from 1 to 9019 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)

9019 / 1 = 9019 (the remainder is 0, so 1 is a divisor of 9019)
9019 / 2 = 4509.5 (the remainder is 1, so 2 is not a divisor of 9019)
9019 / 3 = 3006.3333333333 (the remainder is 1, so 3 is not a divisor of 9019)
...
9019 / 9018 = 1.0001108893324 (the remainder is 1, so 9018 is not a divisor of 9019)
9019 / 9019 = 1 (the remainder is 0, so 9019 is a divisor of 9019)

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 9019 (i.e. 94.968415802308). 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 $\frac{N}{d} = D$ )

9019 / 1 = 9019 (the remainder is 0, so 1 and 9019 are divisors of 9019)
9019 / 2 = 4509.5 (the remainder is 1, so 2 is not a divisor of 9019)
9019 / 3 = 3006.3333333333 (the remainder is 1, so 3 is not a divisor of 9019)
...
9019 / 93 = 96.978494623656 (the remainder is 91, so 93 is not a divisor of 9019)
9019 / 94 = 95.946808510638 (the remainder is 89, so 94 is not a divisor of 9019)