What are the divisors of 9211?

1, 61, 151, 9211

There is a total of 4 positive divisors.
The sum of these divisors is 9424.
The arithmetic mean is 2356.

4 odd divisors

1, 61, 151, 9211

How to compute the divisors of 9211?

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 9211 by each of the numbers from 1 to 9211 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)

9211 / 1 = 9211 (the remainder is 0, so 1 is a divisor of 9211)
9211 / 2 = 4605.5 (the remainder is 1, so 2 is not a divisor of 9211)
9211 / 3 = 3070.3333333333 (the remainder is 1, so 3 is not a divisor of 9211)
...
9211 / 9210 = 1.000108577633 (the remainder is 1, so 9210 is not a divisor of 9211)
9211 / 9211 = 1 (the remainder is 0, so 9211 is a divisor of 9211)

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 9211 (i.e. 95.973954800248). 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 $\frac{N}{d} = D$ )

9211 / 1 = 9211 (the remainder is 0, so 1 and 9211 are divisors of 9211)
9211 / 2 = 4605.5 (the remainder is 1, so 2 is not a divisor of 9211)
9211 / 3 = 3070.3333333333 (the remainder is 1, so 3 is not a divisor of 9211)
...
9211 / 94 = 97.989361702128 (the remainder is 93, so 94 is not a divisor of 9211)
9211 / 95 = 96.957894736842 (the remainder is 91, so 95 is not a divisor of 9211)