What are the divisors of 9641?

1, 31, 311, 9641

There is a total of 4 positive divisors.
The sum of these divisors is 9984.
The arithmetic mean is 2496.

4 odd divisors

1, 31, 311, 9641

How to compute the divisors of 9641?

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 9641 by each of the numbers from 1 to 9641 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)

9641 / 1 = 9641 (the remainder is 0, so 1 is a divisor of 9641)
9641 / 2 = 4820.5 (the remainder is 1, so 2 is not a divisor of 9641)
9641 / 3 = 3213.6666666667 (the remainder is 2, so 3 is not a divisor of 9641)
...
9641 / 9640 = 1.0001037344398 (the remainder is 1, so 9640 is not a divisor of 9641)
9641 / 9641 = 1 (the remainder is 0, so 9641 is a divisor of 9641)

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 9641 (i.e. 98.188594042282). 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 $\frac{N}{d} = D$ )

9641 / 1 = 9641 (the remainder is 0, so 1 and 9641 are divisors of 9641)
9641 / 2 = 4820.5 (the remainder is 1, so 2 is not a divisor of 9641)
9641 / 3 = 3213.6666666667 (the remainder is 2, so 3 is not a divisor of 9641)
...
9641 / 97 = 99.39175257732 (the remainder is 38, so 97 is not a divisor of 9641)
9641 / 98 = 98.377551020408 (the remainder is 37, so 98 is not a divisor of 9641)