What are the divisors of 9621?

1, 3, 9, 1069, 3207, 9621

There is a total of 6 positive divisors.
The sum of these divisors is 13910.
The arithmetic mean is 2318.3333333333.

6 odd divisors

1, 3, 9, 1069, 3207, 9621

How to compute the divisors of 9621?

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 9621 by each of the numbers from 1 to 9621 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)

9621 / 1 = 9621 (the remainder is 0, so 1 is a divisor of 9621)
9621 / 2 = 4810.5 (the remainder is 1, so 2 is not a divisor of 9621)
9621 / 3 = 3207 (the remainder is 0, so 3 is a divisor of 9621)
...
9621 / 9620 = 1.000103950104 (the remainder is 1, so 9620 is not a divisor of 9621)
9621 / 9621 = 1 (the remainder is 0, so 9621 is a divisor of 9621)

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 9621 (i.e. 98.086696345631). 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 $\frac{N}{d} = D$ )

9621 / 1 = 9621 (the remainder is 0, so 1 and 9621 are divisors of 9621)
9621 / 2 = 4810.5 (the remainder is 1, so 2 is not a divisor of 9621)
9621 / 3 = 3207 (the remainder is 0, so 3 and 3207 are divisors of 9621)
...
9621 / 97 = 99.185567010309 (the remainder is 18, so 97 is not a divisor of 9621)
9621 / 98 = 98.173469387755 (the remainder is 17, so 98 is not a divisor of 9621)