What are the divisors of 9217?

1, 13, 709, 9217

There is a total of 4 positive divisors.
The sum of these divisors is 9940.
The arithmetic mean is 2485.

4 odd divisors

1, 13, 709, 9217

How to compute the divisors of 9217?

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 9217 by each of the numbers from 1 to 9217 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)

9217 / 1 = 9217 (the remainder is 0, so 1 is a divisor of 9217)
9217 / 2 = 4608.5 (the remainder is 1, so 2 is not a divisor of 9217)
9217 / 3 = 3072.3333333333 (the remainder is 1, so 3 is not a divisor of 9217)
...
9217 / 9216 = 1.0001085069444 (the remainder is 1, so 9216 is not a divisor of 9217)
9217 / 9217 = 1 (the remainder is 0, so 9217 is a divisor of 9217)

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 9217 (i.e. 96.005208192056). 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 $\frac{N}{d} = D$ )

9217 / 1 = 9217 (the remainder is 0, so 1 and 9217 are divisors of 9217)
9217 / 2 = 4608.5 (the remainder is 1, so 2 is not a divisor of 9217)
9217 / 3 = 3072.3333333333 (the remainder is 1, so 3 is not a divisor of 9217)
...
9217 / 95 = 97.021052631579 (the remainder is 2, so 95 is not a divisor of 9217)
9217 / 96 = 96.010416666667 (the remainder is 1, so 96 is not a divisor of 9217)