What are the divisors of 9061?

1, 13, 17, 41, 221, 533, 697, 9061

There is a total of 8 positive divisors.
The sum of these divisors is 10584.
The arithmetic mean is 1323.

8 odd divisors

1, 13, 17, 41, 221, 533, 697, 9061

How to compute the divisors of 9061?

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 9061 by each of the numbers from 1 to 9061 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)

9061 / 1 = 9061 (the remainder is 0, so 1 is a divisor of 9061)
9061 / 2 = 4530.5 (the remainder is 1, so 2 is not a divisor of 9061)
9061 / 3 = 3020.3333333333 (the remainder is 1, so 3 is not a divisor of 9061)
...
9061 / 9060 = 1.0001103752759 (the remainder is 1, so 9060 is not a divisor of 9061)
9061 / 9061 = 1 (the remainder is 0, so 9061 is a divisor of 9061)

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 9061 (i.e. 95.189285111298). 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 $\frac{N}{d} = D$ )

9061 / 1 = 9061 (the remainder is 0, so 1 and 9061 are divisors of 9061)
9061 / 2 = 4530.5 (the remainder is 1, so 2 is not a divisor of 9061)
9061 / 3 = 3020.3333333333 (the remainder is 1, so 3 is not a divisor of 9061)
...
9061 / 94 = 96.393617021277 (the remainder is 37, so 94 is not a divisor of 9061)
9061 / 95 = 95.378947368421 (the remainder is 36, so 95 is not a divisor of 9061)