What are the divisors of 9201?

1, 3, 3067, 9201

There is a total of 4 positive divisors.
The sum of these divisors is 12272.
The arithmetic mean is 3068.

4 odd divisors

1, 3, 3067, 9201

How to compute the divisors of 9201?

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 9201 by each of the numbers from 1 to 9201 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)

9201 / 1 = 9201 (the remainder is 0, so 1 is a divisor of 9201)
9201 / 2 = 4600.5 (the remainder is 1, so 2 is not a divisor of 9201)
9201 / 3 = 3067 (the remainder is 0, so 3 is a divisor of 9201)
...
9201 / 9200 = 1.0001086956522 (the remainder is 1, so 9200 is not a divisor of 9201)
9201 / 9201 = 1 (the remainder is 0, so 9201 is a divisor of 9201)

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 9201 (i.e. 95.92184318496). 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 $\frac{N}{d} = D$ )

9201 / 1 = 9201 (the remainder is 0, so 1 and 9201 are divisors of 9201)
9201 / 2 = 4600.5 (the remainder is 1, so 2 is not a divisor of 9201)
9201 / 3 = 3067 (the remainder is 0, so 3 and 3067 are divisors of 9201)
...
9201 / 94 = 97.882978723404 (the remainder is 83, so 94 is not a divisor of 9201)
9201 / 95 = 96.852631578947 (the remainder is 81, so 95 is not a divisor of 9201)