What are the divisors of 9032?

1, 2, 4, 8, 1129, 2258, 4516, 9032

There is a total of 8 positive divisors.
The sum of these divisors is 16950.
The arithmetic mean is 2118.75.

6 even divisors

2, 4, 8, 2258, 4516, 9032

2 odd divisors

1, 1129

How to compute the divisors of 9032?

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 9032 by each of the numbers from 1 to 9032 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)

9032 / 1 = 9032 (the remainder is 0, so 1 is a divisor of 9032)
9032 / 2 = 4516 (the remainder is 0, so 2 is a divisor of 9032)
9032 / 3 = 3010.6666666667 (the remainder is 2, so 3 is not a divisor of 9032)
...
9032 / 9031 = 1.0001107297088 (the remainder is 1, so 9031 is not a divisor of 9032)
9032 / 9032 = 1 (the remainder is 0, so 9032 is a divisor of 9032)

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 9032 (i.e. 95.036834964134). 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 $\frac{N}{d} = D$ )

9032 / 1 = 9032 (the remainder is 0, so 1 and 9032 are divisors of 9032)
9032 / 2 = 4516 (the remainder is 0, so 2 and 4516 are divisors of 9032)
9032 / 3 = 3010.6666666667 (the remainder is 2, so 3 is not a divisor of 9032)
...
9032 / 94 = 96.085106382979 (the remainder is 8, so 94 is not a divisor of 9032)
9032 / 95 = 95.073684210526 (the remainder is 7, so 95 is not a divisor of 9032)