What are the divisors of 9626?

1, 2, 4813, 9626

There is a total of 4 positive divisors.
The sum of these divisors is 14442.
The arithmetic mean is 3610.5.

2 even divisors

2, 9626

2 odd divisors

1, 4813

How to compute the divisors of 9626?

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 9626 by each of the numbers from 1 to 9626 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)

9626 / 1 = 9626 (the remainder is 0, so 1 is a divisor of 9626)
9626 / 2 = 4813 (the remainder is 0, so 2 is a divisor of 9626)
9626 / 3 = 3208.6666666667 (the remainder is 2, so 3 is not a divisor of 9626)
...
9626 / 9625 = 1.0001038961039 (the remainder is 1, so 9625 is not a divisor of 9626)
9626 / 9626 = 1 (the remainder is 0, so 9626 is a divisor of 9626)

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 9626 (i.e. 98.112180691288). 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 $\frac{N}{d} = D$ )

9626 / 1 = 9626 (the remainder is 0, so 1 and 9626 are divisors of 9626)
9626 / 2 = 4813 (the remainder is 0, so 2 and 4813 are divisors of 9626)
9626 / 3 = 3208.6666666667 (the remainder is 2, so 3 is not a divisor of 9626)
...
9626 / 97 = 99.237113402062 (the remainder is 23, so 97 is not a divisor of 9626)
9626 / 98 = 98.224489795918 (the remainder is 22, so 98 is not a divisor of 9626)