What are the divisors of 9051?

1, 3, 7, 21, 431, 1293, 3017, 9051

There is a total of 8 positive divisors.
The sum of these divisors is 13824.
The arithmetic mean is 1728.

8 odd divisors

1, 3, 7, 21, 431, 1293, 3017, 9051

How to compute the divisors of 9051?

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 9051 by each of the numbers from 1 to 9051 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)

9051 / 1 = 9051 (the remainder is 0, so 1 is a divisor of 9051)
9051 / 2 = 4525.5 (the remainder is 1, so 2 is not a divisor of 9051)
9051 / 3 = 3017 (the remainder is 0, so 3 is a divisor of 9051)
...
9051 / 9050 = 1.0001104972376 (the remainder is 1, so 9050 is not a divisor of 9051)
9051 / 9051 = 1 (the remainder is 0, so 9051 is a divisor of 9051)

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 9051 (i.e. 95.136743690332). 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 $\frac{N}{d} = D$ )

9051 / 1 = 9051 (the remainder is 0, so 1 and 9051 are divisors of 9051)
9051 / 2 = 4525.5 (the remainder is 1, so 2 is not a divisor of 9051)
9051 / 3 = 3017 (the remainder is 0, so 3 and 3017 are divisors of 9051)
...
9051 / 94 = 96.287234042553 (the remainder is 27, so 94 is not a divisor of 9051)
9051 / 95 = 95.273684210526 (the remainder is 26, so 95 is not a divisor of 9051)