What are the divisors of 9205?

1, 5, 7, 35, 263, 1315, 1841, 9205

There is a total of 8 positive divisors.
The sum of these divisors is 12672.
The arithmetic mean is 1584.

8 odd divisors

1, 5, 7, 35, 263, 1315, 1841, 9205

How to compute the divisors of 9205?

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 9205 by each of the numbers from 1 to 9205 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)

9205 / 1 = 9205 (the remainder is 0, so 1 is a divisor of 9205)
9205 / 2 = 4602.5 (the remainder is 1, so 2 is not a divisor of 9205)
9205 / 3 = 3068.3333333333 (the remainder is 1, so 3 is not a divisor of 9205)
...
9205 / 9204 = 1.0001086484137 (the remainder is 1, so 9204 is not a divisor of 9205)
9205 / 9205 = 1 (the remainder is 0, so 9205 is a divisor of 9205)

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 9205 (i.e. 95.942691227628). 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 $\frac{N}{d} = D$ )

9205 / 1 = 9205 (the remainder is 0, so 1 and 9205 are divisors of 9205)
9205 / 2 = 4602.5 (the remainder is 1, so 2 is not a divisor of 9205)
9205 / 3 = 3068.3333333333 (the remainder is 1, so 3 is not a divisor of 9205)
...
9205 / 94 = 97.925531914894 (the remainder is 87, so 94 is not a divisor of 9205)
9205 / 95 = 96.894736842105 (the remainder is 85, so 95 is not a divisor of 9205)