What are the divisors of 9627?

1, 3, 3209, 9627

There is a total of 4 positive divisors.
The sum of these divisors is 12840.
The arithmetic mean is 3210.

4 odd divisors

1, 3, 3209, 9627

How to compute the divisors of 9627?

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 9627 by each of the numbers from 1 to 9627 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)

9627 / 1 = 9627 (the remainder is 0, so 1 is a divisor of 9627)
9627 / 2 = 4813.5 (the remainder is 1, so 2 is not a divisor of 9627)
9627 / 3 = 3209 (the remainder is 0, so 3 is a divisor of 9627)
...
9627 / 9626 = 1.0001038853106 (the remainder is 1, so 9626 is not a divisor of 9627)
9627 / 9627 = 1 (the remainder is 0, so 9627 is a divisor of 9627)

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 9627 (i.e. 98.117276766123). 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 $\frac{N}{d} = D$ )

9627 / 1 = 9627 (the remainder is 0, so 1 and 9627 are divisors of 9627)
9627 / 2 = 4813.5 (the remainder is 1, so 2 is not a divisor of 9627)
9627 / 3 = 3209 (the remainder is 0, so 3 and 3209 are divisors of 9627)
...
9627 / 97 = 99.247422680412 (the remainder is 24, so 97 is not a divisor of 9627)
9627 / 98 = 98.234693877551 (the remainder is 23, so 98 is not a divisor of 9627)