What are the divisors of 9622?

1, 2, 17, 34, 283, 566, 4811, 9622

There is a total of 8 positive divisors.
The sum of these divisors is 15336.
The arithmetic mean is 1917.

4 even divisors

2, 34, 566, 9622

4 odd divisors

1, 17, 283, 4811

How to compute the divisors of 9622?

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 9622 by each of the numbers from 1 to 9622 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)

9622 / 1 = 9622 (the remainder is 0, so 1 is a divisor of 9622)
9622 / 2 = 4811 (the remainder is 0, so 2 is a divisor of 9622)
9622 / 3 = 3207.3333333333 (the remainder is 1, so 3 is not a divisor of 9622)
...
9622 / 9621 = 1.0001039392994 (the remainder is 1, so 9621 is not a divisor of 9622)
9622 / 9622 = 1 (the remainder is 0, so 9622 is a divisor of 9622)

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 9622 (i.e. 98.091793744431). 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 $\frac{N}{d} = D$ )

9622 / 1 = 9622 (the remainder is 0, so 1 and 9622 are divisors of 9622)
9622 / 2 = 4811 (the remainder is 0, so 2 and 4811 are divisors of 9622)
9622 / 3 = 3207.3333333333 (the remainder is 1, so 3 is not a divisor of 9622)
...
9622 / 97 = 99.19587628866 (the remainder is 19, so 97 is not a divisor of 9622)
9622 / 98 = 98.183673469388 (the remainder is 18, so 98 is not a divisor of 9622)