What are the divisors of 9647?

1, 11, 877, 9647

There is a total of 4 positive divisors.
The sum of these divisors is 10536.
The arithmetic mean is 2634.

4 odd divisors

1, 11, 877, 9647

How to compute the divisors of 9647?

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 9647 by each of the numbers from 1 to 9647 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)

9647 / 1 = 9647 (the remainder is 0, so 1 is a divisor of 9647)
9647 / 2 = 4823.5 (the remainder is 1, so 2 is not a divisor of 9647)
9647 / 3 = 3215.6666666667 (the remainder is 2, so 3 is not a divisor of 9647)
...
9647 / 9646 = 1.000103669915 (the remainder is 1, so 9646 is not a divisor of 9647)
9647 / 9647 = 1 (the remainder is 0, so 9647 is a divisor of 9647)

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 9647 (i.e. 98.219142737045). 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 $\frac{N}{d} = D$ )

9647 / 1 = 9647 (the remainder is 0, so 1 and 9647 are divisors of 9647)
9647 / 2 = 4823.5 (the remainder is 1, so 2 is not a divisor of 9647)
9647 / 3 = 3215.6666666667 (the remainder is 2, so 3 is not a divisor of 9647)
...
9647 / 97 = 99.453608247423 (the remainder is 44, so 97 is not a divisor of 9647)
9647 / 98 = 98.438775510204 (the remainder is 43, so 98 is not a divisor of 9647)