What are the divisors of 9029?

1, 9029

There is a total of 2 positive divisors.
The sum of these divisors is 9030.
The arithmetic mean is 4515.

2 odd divisors

1, 9029

How to compute the divisors of 9029?

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 9029 by each of the numbers from 1 to 9029 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)

9029 / 1 = 9029 (the remainder is 0, so 1 is a divisor of 9029)
9029 / 2 = 4514.5 (the remainder is 1, so 2 is not a divisor of 9029)
9029 / 3 = 3009.6666666667 (the remainder is 2, so 3 is not a divisor of 9029)
...
9029 / 9028 = 1.0001107665042 (the remainder is 1, so 9028 is not a divisor of 9029)
9029 / 9029 = 1 (the remainder is 0, so 9029 is a divisor of 9029)

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 9029 (i.e. 95.021050299394). 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 $\frac{N}{d} = D$ )

9029 / 1 = 9029 (the remainder is 0, so 1 and 9029 are divisors of 9029)
9029 / 2 = 4514.5 (the remainder is 1, so 2 is not a divisor of 9029)
9029 / 3 = 3009.6666666667 (the remainder is 2, so 3 is not a divisor of 9029)
...
9029 / 94 = 96.053191489362 (the remainder is 5, so 94 is not a divisor of 9029)
9029 / 95 = 95.042105263158 (the remainder is 4, so 95 is not a divisor of 9029)