What are the divisors of 9171?

1, 3, 9, 1019, 3057, 9171

There is a total of 6 positive divisors.
The sum of these divisors is 13260.
The arithmetic mean is 2210.

6 odd divisors

1, 3, 9, 1019, 3057, 9171

How to compute the divisors of 9171?

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 9171 by each of the numbers from 1 to 9171 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)

9171 / 1 = 9171 (the remainder is 0, so 1 is a divisor of 9171)
9171 / 2 = 4585.5 (the remainder is 1, so 2 is not a divisor of 9171)
9171 / 3 = 3057 (the remainder is 0, so 3 is a divisor of 9171)
...
9171 / 9170 = 1.0001090512541 (the remainder is 1, so 9170 is not a divisor of 9171)
9171 / 9171 = 1 (the remainder is 0, so 9171 is a divisor of 9171)

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 9171 (i.e. 95.765338197074). 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 $\frac{N}{d} = D$ )

9171 / 1 = 9171 (the remainder is 0, so 1 and 9171 are divisors of 9171)
9171 / 2 = 4585.5 (the remainder is 1, so 2 is not a divisor of 9171)
9171 / 3 = 3057 (the remainder is 0, so 3 and 3057 are divisors of 9171)
...
9171 / 94 = 97.563829787234 (the remainder is 53, so 94 is not a divisor of 9171)
9171 / 95 = 96.536842105263 (the remainder is 51, so 95 is not a divisor of 9171)