What are the divisors of 9646?

1, 2, 7, 13, 14, 26, 53, 91, 106, 182, 371, 689, 742, 1378, 4823, 9646

There is a total of 16 positive divisors.
The sum of these divisors is 18144.
The arithmetic mean is 1134.

8 even divisors

2, 14, 26, 106, 182, 742, 1378, 9646

8 odd divisors

1, 7, 13, 53, 91, 371, 689, 4823

How to compute the divisors of 9646?

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 9646 by each of the numbers from 1 to 9646 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)

9646 / 1 = 9646 (the remainder is 0, so 1 is a divisor of 9646)
9646 / 2 = 4823 (the remainder is 0, so 2 is a divisor of 9646)
9646 / 3 = 3215.3333333333 (the remainder is 1, so 3 is not a divisor of 9646)
...
9646 / 9645 = 1.0001036806636 (the remainder is 1, so 9645 is not a divisor of 9646)
9646 / 9646 = 1 (the remainder is 0, so 9646 is a divisor of 9646)

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 9646 (i.e. 98.214051947774). 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 $\frac{N}{d} = D$ )

9646 / 1 = 9646 (the remainder is 0, so 1 and 9646 are divisors of 9646)
9646 / 2 = 4823 (the remainder is 0, so 2 and 4823 are divisors of 9646)
9646 / 3 = 3215.3333333333 (the remainder is 1, so 3 is not a divisor of 9646)
...
9646 / 97 = 99.443298969072 (the remainder is 43, so 97 is not a divisor of 9646)
9646 / 98 = 98.428571428571 (the remainder is 42, so 98 is not a divisor of 9646)