What are the divisors of 9634?

1, 2, 4817, 9634

There is a total of 4 positive divisors.
The sum of these divisors is 14454.
The arithmetic mean is 3613.5.

2 even divisors

2, 9634

2 odd divisors

1, 4817

How to compute the divisors of 9634?

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 9634 by each of the numbers from 1 to 9634 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)

9634 / 1 = 9634 (the remainder is 0, so 1 is a divisor of 9634)
9634 / 2 = 4817 (the remainder is 0, so 2 is a divisor of 9634)
9634 / 3 = 3211.3333333333 (the remainder is 1, so 3 is not a divisor of 9634)
...
9634 / 9633 = 1.0001038098204 (the remainder is 1, so 9633 is not a divisor of 9634)
9634 / 9634 = 1 (the remainder is 0, so 9634 is a divisor of 9634)

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 9634 (i.e. 98.152941881535). 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 $\frac{N}{d} = D$ )

9634 / 1 = 9634 (the remainder is 0, so 1 and 9634 are divisors of 9634)
9634 / 2 = 4817 (the remainder is 0, so 2 and 4817 are divisors of 9634)
9634 / 3 = 3211.3333333333 (the remainder is 1, so 3 is not a divisor of 9634)
...
9634 / 97 = 99.319587628866 (the remainder is 31, so 97 is not a divisor of 9634)
9634 / 98 = 98.30612244898 (the remainder is 30, so 98 is not a divisor of 9634)