What are the divisors of 9021?

1, 3, 31, 93, 97, 291, 3007, 9021

There is a total of 8 positive divisors.
The sum of these divisors is 12544.
The arithmetic mean is 1568.

8 odd divisors

1, 3, 31, 93, 97, 291, 3007, 9021

How to compute the divisors of 9021?

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 9021 by each of the numbers from 1 to 9021 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)

9021 / 1 = 9021 (the remainder is 0, so 1 is a divisor of 9021)
9021 / 2 = 4510.5 (the remainder is 1, so 2 is not a divisor of 9021)
9021 / 3 = 3007 (the remainder is 0, so 3 is a divisor of 9021)
...
9021 / 9020 = 1.000110864745 (the remainder is 1, so 9020 is not a divisor of 9021)
9021 / 9021 = 1 (the remainder is 0, so 9021 is a divisor of 9021)

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 9021 (i.e. 94.978945035202). 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 $\frac{N}{d} = D$ )

9021 / 1 = 9021 (the remainder is 0, so 1 and 9021 are divisors of 9021)
9021 / 2 = 4510.5 (the remainder is 1, so 2 is not a divisor of 9021)
9021 / 3 = 3007 (the remainder is 0, so 3 and 3007 are divisors of 9021)
...
9021 / 93 = 97 (the remainder is 0, so 93 and 97 are divisors of 9021)
9021 / 94 = 95.968085106383 (the remainder is 91, so 94 is not a divisor of 9021)