What are the divisors of 9613?

1, 9613

There is a total of 2 positive divisors.
The sum of these divisors is 9614.
The arithmetic mean is 4807.

2 odd divisors

1, 9613

How to compute the divisors of 9613?

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 9613 by each of the numbers from 1 to 9613 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)

9613 / 1 = 9613 (the remainder is 0, so 1 is a divisor of 9613)
9613 / 2 = 4806.5 (the remainder is 1, so 2 is not a divisor of 9613)
9613 / 3 = 3204.3333333333 (the remainder is 1, so 3 is not a divisor of 9613)
...
9613 / 9612 = 1.0001040366209 (the remainder is 1, so 9612 is not a divisor of 9613)
9613 / 9613 = 1 (the remainder is 0, so 9613 is a divisor of 9613)

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 9613 (i.e. 98.04590761475). 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 $\frac{N}{d} = D$ )

9613 / 1 = 9613 (the remainder is 0, so 1 and 9613 are divisors of 9613)
9613 / 2 = 4806.5 (the remainder is 1, so 2 is not a divisor of 9613)
9613 / 3 = 3204.3333333333 (the remainder is 1, so 3 is not a divisor of 9613)
...
9613 / 97 = 99.103092783505 (the remainder is 10, so 97 is not a divisor of 9613)
9613 / 98 = 98.091836734694 (the remainder is 9, so 98 is not a divisor of 9613)