What are the divisors of 9121?

1, 7, 1303, 9121

There is a total of 4 positive divisors.
The sum of these divisors is 10432.
The arithmetic mean is 2608.

4 odd divisors

1, 7, 1303, 9121

How to compute the divisors of 9121?

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 9121 by each of the numbers from 1 to 9121 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)

9121 / 1 = 9121 (the remainder is 0, so 1 is a divisor of 9121)
9121 / 2 = 4560.5 (the remainder is 1, so 2 is not a divisor of 9121)
9121 / 3 = 3040.3333333333 (the remainder is 1, so 3 is not a divisor of 9121)
...
9121 / 9120 = 1.0001096491228 (the remainder is 1, so 9120 is not a divisor of 9121)
9121 / 9121 = 1 (the remainder is 0, so 9121 is a divisor of 9121)

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 9121 (i.e. 95.503926620846). 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 $\frac{N}{d} = D$ )

9121 / 1 = 9121 (the remainder is 0, so 1 and 9121 are divisors of 9121)
9121 / 2 = 4560.5 (the remainder is 1, so 2 is not a divisor of 9121)
9121 / 3 = 3040.3333333333 (the remainder is 1, so 3 is not a divisor of 9121)
...
9121 / 94 = 97.031914893617 (the remainder is 3, so 94 is not a divisor of 9121)
9121 / 95 = 96.010526315789 (the remainder is 1, so 95 is not a divisor of 9121)