What are the divisors of 9635?

1, 5, 41, 47, 205, 235, 1927, 9635

There is a total of 8 positive divisors.
The sum of these divisors is 12096.
The arithmetic mean is 1512.

8 odd divisors

1, 5, 41, 47, 205, 235, 1927, 9635

How to compute the divisors of 9635?

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 9635 by each of the numbers from 1 to 9635 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)

9635 / 1 = 9635 (the remainder is 0, so 1 is a divisor of 9635)
9635 / 2 = 4817.5 (the remainder is 1, so 2 is not a divisor of 9635)
9635 / 3 = 3211.6666666667 (the remainder is 2, so 3 is not a divisor of 9635)
...
9635 / 9634 = 1.000103799045 (the remainder is 1, so 9634 is not a divisor of 9635)
9635 / 9635 = 1 (the remainder is 0, so 9635 is a divisor of 9635)

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 9635 (i.e. 98.15803584017). 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 $\frac{N}{d} = D$ )

9635 / 1 = 9635 (the remainder is 0, so 1 and 9635 are divisors of 9635)
9635 / 2 = 4817.5 (the remainder is 1, so 2 is not a divisor of 9635)
9635 / 3 = 3211.6666666667 (the remainder is 2, so 3 is not a divisor of 9635)
...
9635 / 97 = 99.329896907216 (the remainder is 32, so 97 is not a divisor of 9635)
9635 / 98 = 98.316326530612 (the remainder is 31, so 98 is not a divisor of 9635)