What are the divisors of 9633?

1, 3, 13, 19, 39, 57, 169, 247, 507, 741, 3211, 9633

There is a total of 12 positive divisors.
The sum of these divisors is 14640.
The arithmetic mean is 1220.

12 odd divisors

1, 3, 13, 19, 39, 57, 169, 247, 507, 741, 3211, 9633

How to compute the divisors of 9633?

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 9633 by each of the numbers from 1 to 9633 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)

9633 / 1 = 9633 (the remainder is 0, so 1 is a divisor of 9633)
9633 / 2 = 4816.5 (the remainder is 1, so 2 is not a divisor of 9633)
9633 / 3 = 3211 (the remainder is 0, so 3 is a divisor of 9633)
...
9633 / 9632 = 1.000103820598 (the remainder is 1, so 9632 is not a divisor of 9633)
9633 / 9633 = 1 (the remainder is 0, so 9633 is a divisor of 9633)

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 9633 (i.e. 98.14784765852). 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 $\frac{N}{d} = D$ )

9633 / 1 = 9633 (the remainder is 0, so 1 and 9633 are divisors of 9633)
9633 / 2 = 4816.5 (the remainder is 1, so 2 is not a divisor of 9633)
9633 / 3 = 3211 (the remainder is 0, so 3 and 3211 are divisors of 9633)
...
9633 / 97 = 99.309278350515 (the remainder is 30, so 97 is not a divisor of 9633)
9633 / 98 = 98.295918367347 (the remainder is 29, so 98 is not a divisor of 9633)