What are the divisors of 9619?

1, 9619

There is a total of 2 positive divisors.
The sum of these divisors is 9620.
The arithmetic mean is 4810.

2 odd divisors

1, 9619

How to compute the divisors of 9619?

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 9619 by each of the numbers from 1 to 9619 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)

9619 / 1 = 9619 (the remainder is 0, so 1 is a divisor of 9619)
9619 / 2 = 4809.5 (the remainder is 1, so 2 is not a divisor of 9619)
9619 / 3 = 3206.3333333333 (the remainder is 1, so 3 is not a divisor of 9619)
...
9619 / 9618 = 1.0001039717197 (the remainder is 1, so 9618 is not a divisor of 9619)
9619 / 9619 = 1 (the remainder is 0, so 9619 is a divisor of 9619)

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 9619 (i.e. 98.076500753239). 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 $\frac{N}{d} = D$ )

9619 / 1 = 9619 (the remainder is 0, so 1 and 9619 are divisors of 9619)
9619 / 2 = 4809.5 (the remainder is 1, so 2 is not a divisor of 9619)
9619 / 3 = 3206.3333333333 (the remainder is 1, so 3 is not a divisor of 9619)
...
9619 / 97 = 99.164948453608 (the remainder is 16, so 97 is not a divisor of 9619)
9619 / 98 = 98.15306122449 (the remainder is 15, so 98 is not a divisor of 9619)