What are the divisors of 9241?

1, 9241

There is a total of 2 positive divisors.
The sum of these divisors is 9242.
The arithmetic mean is 4621.

2 odd divisors

1, 9241

How to compute the divisors of 9241?

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 9241 by each of the numbers from 1 to 9241 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)

9241 / 1 = 9241 (the remainder is 0, so 1 is a divisor of 9241)
9241 / 2 = 4620.5 (the remainder is 1, so 2 is not a divisor of 9241)
9241 / 3 = 3080.3333333333 (the remainder is 1, so 3 is not a divisor of 9241)
...
9241 / 9240 = 1.0001082251082 (the remainder is 1, so 9240 is not a divisor of 9241)
9241 / 9241 = 1 (the remainder is 0, so 9241 is a divisor of 9241)

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 9241 (i.e. 96.130120149722). 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 $\frac{N}{d} = D$ )

9241 / 1 = 9241 (the remainder is 0, so 1 and 9241 are divisors of 9241)
9241 / 2 = 4620.5 (the remainder is 1, so 2 is not a divisor of 9241)
9241 / 3 = 3080.3333333333 (the remainder is 1, so 3 is not a divisor of 9241)
...
9241 / 95 = 97.273684210526 (the remainder is 26, so 95 is not a divisor of 9241)
9241 / 96 = 96.260416666667 (the remainder is 25, so 96 is not a divisor of 9241)