What are the divisors of 9639?

1, 3, 7, 9, 17, 21, 27, 51, 63, 81, 119, 153, 189, 357, 459, 567, 1071, 1377, 3213, 9639

There is a total of 20 positive divisors.
The sum of these divisors is 17424.
The arithmetic mean is 871.2.

20 odd divisors

1, 3, 7, 9, 17, 21, 27, 51, 63, 81, 119, 153, 189, 357, 459, 567, 1071, 1377, 3213, 9639

How to compute the divisors of 9639?

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 9639 by each of the numbers from 1 to 9639 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)

9639 / 1 = 9639 (the remainder is 0, so 1 is a divisor of 9639)
9639 / 2 = 4819.5 (the remainder is 1, so 2 is not a divisor of 9639)
9639 / 3 = 3213 (the remainder is 0, so 3 is a divisor of 9639)
...
9639 / 9638 = 1.000103755966 (the remainder is 1, so 9638 is not a divisor of 9639)
9639 / 9639 = 1 (the remainder is 0, so 9639 is a divisor of 9639)

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 9639 (i.e. 98.178409031721). 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 $\frac{N}{d} = D$ )

9639 / 1 = 9639 (the remainder is 0, so 1 and 9639 are divisors of 9639)
9639 / 2 = 4819.5 (the remainder is 1, so 2 is not a divisor of 9639)
9639 / 3 = 3213 (the remainder is 0, so 3 and 3213 are divisors of 9639)
...
9639 / 97 = 99.371134020619 (the remainder is 36, so 97 is not a divisor of 9639)
9639 / 98 = 98.357142857143 (the remainder is 35, so 98 is not a divisor of 9639)