What are the divisors of 9597?

1, 3, 7, 21, 457, 1371, 3199, 9597

There is a total of 8 positive divisors.
The sum of these divisors is 14656.
The arithmetic mean is 1832.

8 odd divisors

1, 3, 7, 21, 457, 1371, 3199, 9597

How to compute the divisors of 9597?

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 9597 by each of the numbers from 1 to 9597 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)

9597 / 1 = 9597 (the remainder is 0, so 1 is a divisor of 9597)
9597 / 2 = 4798.5 (the remainder is 1, so 2 is not a divisor of 9597)
9597 / 3 = 3199 (the remainder is 0, so 3 is a divisor of 9597)
...
9597 / 9596 = 1.0001042100875 (the remainder is 1, so 9596 is not a divisor of 9597)
9597 / 9597 = 1 (the remainder is 0, so 9597 is a divisor of 9597)

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 9597 (i.e. 97.964279204208). 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 $\frac{N}{d} = D$ )

9597 / 1 = 9597 (the remainder is 0, so 1 and 9597 are divisors of 9597)
9597 / 2 = 4798.5 (the remainder is 1, so 2 is not a divisor of 9597)
9597 / 3 = 3199 (the remainder is 0, so 3 and 3199 are divisors of 9597)
...
9597 / 96 = 99.96875 (the remainder is 93, so 96 is not a divisor of 9597)
9597 / 97 = 98.938144329897 (the remainder is 91, so 97 is not a divisor of 9597)