What are the divisors of 9031?

1, 11, 821, 9031

There is a total of 4 positive divisors.
The sum of these divisors is 9864.
The arithmetic mean is 2466.

4 odd divisors

1, 11, 821, 9031

How to compute the divisors of 9031?

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 9031 by each of the numbers from 1 to 9031 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)

9031 / 1 = 9031 (the remainder is 0, so 1 is a divisor of 9031)
9031 / 2 = 4515.5 (the remainder is 1, so 2 is not a divisor of 9031)
9031 / 3 = 3010.3333333333 (the remainder is 1, so 3 is not a divisor of 9031)
...
9031 / 9030 = 1.0001107419712 (the remainder is 1, so 9030 is not a divisor of 9031)
9031 / 9031 = 1 (the remainder is 0, so 9031 is a divisor of 9031)

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 9031 (i.e. 95.031573700534). 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 $\frac{N}{d} = D$ )

9031 / 1 = 9031 (the remainder is 0, so 1 and 9031 are divisors of 9031)
9031 / 2 = 4515.5 (the remainder is 1, so 2 is not a divisor of 9031)
9031 / 3 = 3010.3333333333 (the remainder is 1, so 3 is not a divisor of 9031)
...
9031 / 94 = 96.074468085106 (the remainder is 7, so 94 is not a divisor of 9031)
9031 / 95 = 95.063157894737 (the remainder is 6, so 95 is not a divisor of 9031)