What are the divisors of 9113?

1, 13, 701, 9113

There is a total of 4 positive divisors.
The sum of these divisors is 9828.
The arithmetic mean is 2457.

4 odd divisors

1, 13, 701, 9113

How to compute the divisors of 9113?

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 9113 by each of the numbers from 1 to 9113 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)

9113 / 1 = 9113 (the remainder is 0, so 1 is a divisor of 9113)
9113 / 2 = 4556.5 (the remainder is 1, so 2 is not a divisor of 9113)
9113 / 3 = 3037.6666666667 (the remainder is 2, so 3 is not a divisor of 9113)
...
9113 / 9112 = 1.0001097453907 (the remainder is 1, so 9112 is not a divisor of 9113)
9113 / 9113 = 1 (the remainder is 0, so 9113 is a divisor of 9113)

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 9113 (i.e. 95.462034338265). 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 $\frac{N}{d} = D$ )

9113 / 1 = 9113 (the remainder is 0, so 1 and 9113 are divisors of 9113)
9113 / 2 = 4556.5 (the remainder is 1, so 2 is not a divisor of 9113)
9113 / 3 = 3037.6666666667 (the remainder is 2, so 3 is not a divisor of 9113)
...
9113 / 94 = 96.946808510638 (the remainder is 89, so 94 is not a divisor of 9113)
9113 / 95 = 95.926315789474 (the remainder is 88, so 95 is not a divisor of 9113)