What are the divisors of 9644?

1, 2, 4, 2411, 4822, 9644

There is a total of 6 positive divisors.
The sum of these divisors is 16884.
The arithmetic mean is 2814.

4 even divisors

2, 4, 4822, 9644

2 odd divisors

1, 2411

How to compute the divisors of 9644?

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 9644 by each of the numbers from 1 to 9644 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)

9644 / 1 = 9644 (the remainder is 0, so 1 is a divisor of 9644)
9644 / 2 = 4822 (the remainder is 0, so 2 is a divisor of 9644)
9644 / 3 = 3214.6666666667 (the remainder is 2, so 3 is not a divisor of 9644)
...
9644 / 9643 = 1.0001037021674 (the remainder is 1, so 9643 is not a divisor of 9644)
9644 / 9644 = 1 (the remainder is 0, so 9644 is a divisor of 9644)

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 9644 (i.e. 98.203869577527). 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 $\frac{N}{d} = D$ )

9644 / 1 = 9644 (the remainder is 0, so 1 and 9644 are divisors of 9644)
9644 / 2 = 4822 (the remainder is 0, so 2 and 4822 are divisors of 9644)
9644 / 3 = 3214.6666666667 (the remainder is 2, so 3 is not a divisor of 9644)
...
9644 / 97 = 99.422680412371 (the remainder is 41, so 97 is not a divisor of 9644)
9644 / 98 = 98.408163265306 (the remainder is 40, so 98 is not a divisor of 9644)