What are the divisors of 9047?

1, 83, 109, 9047

There is a total of 4 positive divisors.
The sum of these divisors is 9240.
The arithmetic mean is 2310.

4 odd divisors

1, 83, 109, 9047

How to compute the divisors of 9047?

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 9047 by each of the numbers from 1 to 9047 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)

9047 / 1 = 9047 (the remainder is 0, so 1 is a divisor of 9047)
9047 / 2 = 4523.5 (the remainder is 1, so 2 is not a divisor of 9047)
9047 / 3 = 3015.6666666667 (the remainder is 2, so 3 is not a divisor of 9047)
...
9047 / 9046 = 1.0001105460977 (the remainder is 1, so 9046 is not a divisor of 9047)
9047 / 9047 = 1 (the remainder is 0, so 9047 is a divisor of 9047)

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 9047 (i.e. 95.115718995337). 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 $\frac{N}{d} = D$ )

9047 / 1 = 9047 (the remainder is 0, so 1 and 9047 are divisors of 9047)
9047 / 2 = 4523.5 (the remainder is 1, so 2 is not a divisor of 9047)
9047 / 3 = 3015.6666666667 (the remainder is 2, so 3 is not a divisor of 9047)
...
9047 / 94 = 96.244680851064 (the remainder is 23, so 94 is not a divisor of 9047)
9047 / 95 = 95.231578947368 (the remainder is 22, so 95 is not a divisor of 9047)