What are the divisors of 9101?

1, 19, 479, 9101

There is a total of 4 positive divisors.
The sum of these divisors is 9600.
The arithmetic mean is 2400.

4 odd divisors

1, 19, 479, 9101

How to compute the divisors of 9101?

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 9101 by each of the numbers from 1 to 9101 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)

9101 / 1 = 9101 (the remainder is 0, so 1 is a divisor of 9101)
9101 / 2 = 4550.5 (the remainder is 1, so 2 is not a divisor of 9101)
9101 / 3 = 3033.6666666667 (the remainder is 2, so 3 is not a divisor of 9101)
...
9101 / 9100 = 1.0001098901099 (the remainder is 1, so 9100 is not a divisor of 9101)
9101 / 9101 = 1 (the remainder is 0, so 9101 is a divisor of 9101)

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 9101 (i.e. 95.399161421891). 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 $\frac{N}{d} = D$ )

9101 / 1 = 9101 (the remainder is 0, so 1 and 9101 are divisors of 9101)
9101 / 2 = 4550.5 (the remainder is 1, so 2 is not a divisor of 9101)
9101 / 3 = 3033.6666666667 (the remainder is 2, so 3 is not a divisor of 9101)
...
9101 / 94 = 96.81914893617 (the remainder is 77, so 94 is not a divisor of 9101)
9101 / 95 = 95.8 (the remainder is 76, so 95 is not a divisor of 9101)