What are the divisors of 9615?

1, 3, 5, 15, 641, 1923, 3205, 9615

There is a total of 8 positive divisors.
The sum of these divisors is 15408.
The arithmetic mean is 1926.

8 odd divisors

1, 3, 5, 15, 641, 1923, 3205, 9615

How to compute the divisors of 9615?

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 9615 by each of the numbers from 1 to 9615 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)

9615 / 1 = 9615 (the remainder is 0, so 1 is a divisor of 9615)
9615 / 2 = 4807.5 (the remainder is 1, so 2 is not a divisor of 9615)
9615 / 3 = 3205 (the remainder is 0, so 3 is a divisor of 9615)
...
9615 / 9614 = 1.0001040149782 (the remainder is 1, so 9614 is not a divisor of 9615)
9615 / 9615 = 1 (the remainder is 0, so 9615 is a divisor of 9615)

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 9615 (i.e. 98.056106388129). 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 $\frac{N}{d} = D$ )

9615 / 1 = 9615 (the remainder is 0, so 1 and 9615 are divisors of 9615)
9615 / 2 = 4807.5 (the remainder is 1, so 2 is not a divisor of 9615)
9615 / 3 = 3205 (the remainder is 0, so 3 and 3205 are divisors of 9615)
...
9615 / 97 = 99.123711340206 (the remainder is 12, so 97 is not a divisor of 9615)
9615 / 98 = 98.112244897959 (the remainder is 11, so 98 is not a divisor of 9615)