What are the divisors of 9629?

1, 9629

There is a total of 2 positive divisors.
The sum of these divisors is 9630.
The arithmetic mean is 4815.

2 odd divisors

1, 9629

How to compute the divisors of 9629?

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 9629 by each of the numbers from 1 to 9629 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)

9629 / 1 = 9629 (the remainder is 0, so 1 is a divisor of 9629)
9629 / 2 = 4814.5 (the remainder is 1, so 2 is not a divisor of 9629)
9629 / 3 = 3209.6666666667 (the remainder is 2, so 3 is not a divisor of 9629)
...
9629 / 9628 = 1.0001038637308 (the remainder is 1, so 9628 is not a divisor of 9629)
9629 / 9629 = 1 (the remainder is 0, so 9629 is a divisor of 9629)

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 9629 (i.e. 98.127468121826). 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 $\frac{N}{d} = D$ )

9629 / 1 = 9629 (the remainder is 0, so 1 and 9629 are divisors of 9629)
9629 / 2 = 4814.5 (the remainder is 1, so 2 is not a divisor of 9629)
9629 / 3 = 3209.6666666667 (the remainder is 2, so 3 is not a divisor of 9629)
...
9629 / 97 = 99.268041237113 (the remainder is 26, so 97 is not a divisor of 9629)
9629 / 98 = 98.255102040816 (the remainder is 25, so 98 is not a divisor of 9629)