What are the divisors of 9147?

1, 3, 3049, 9147

There is a total of 4 positive divisors.
The sum of these divisors is 12200.
The arithmetic mean is 3050.

4 odd divisors

1, 3, 3049, 9147

How to compute the divisors of 9147?

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 9147 by each of the numbers from 1 to 9147 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)

9147 / 1 = 9147 (the remainder is 0, so 1 is a divisor of 9147)
9147 / 2 = 4573.5 (the remainder is 1, so 2 is not a divisor of 9147)
9147 / 3 = 3049 (the remainder is 0, so 3 is a divisor of 9147)
...
9147 / 9146 = 1.0001093374153 (the remainder is 1, so 9146 is not a divisor of 9147)
9147 / 9147 = 1 (the remainder is 0, so 9147 is a divisor of 9147)

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 9147 (i.e. 95.639949811781). 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 $\frac{N}{d} = D$ )

9147 / 1 = 9147 (the remainder is 0, so 1 and 9147 are divisors of 9147)
9147 / 2 = 4573.5 (the remainder is 1, so 2 is not a divisor of 9147)
9147 / 3 = 3049 (the remainder is 0, so 3 and 3049 are divisors of 9147)
...
9147 / 94 = 97.308510638298 (the remainder is 29, so 94 is not a divisor of 9147)
9147 / 95 = 96.284210526316 (the remainder is 27, so 95 is not a divisor of 9147)