What are the divisors of 9038?

1, 2, 4519, 9038

There is a total of 4 positive divisors.
The sum of these divisors is 13560.
The arithmetic mean is 3390.

2 even divisors

2, 9038

2 odd divisors

1, 4519

How to compute the divisors of 9038?

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 9038 by each of the numbers from 1 to 9038 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)

9038 / 1 = 9038 (the remainder is 0, so 1 is a divisor of 9038)
9038 / 2 = 4519 (the remainder is 0, so 2 is a divisor of 9038)
9038 / 3 = 3012.6666666667 (the remainder is 2, so 3 is not a divisor of 9038)
...
9038 / 9037 = 1.0001106561912 (the remainder is 1, so 9037 is not a divisor of 9038)
9038 / 9038 = 1 (the remainder is 0, so 9038 is a divisor of 9038)

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 9038 (i.e. 95.068396431201). 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 $\frac{N}{d} = D$ )

9038 / 1 = 9038 (the remainder is 0, so 1 and 9038 are divisors of 9038)
9038 / 2 = 4519 (the remainder is 0, so 2 and 4519 are divisors of 9038)
9038 / 3 = 3012.6666666667 (the remainder is 2, so 3 is not a divisor of 9038)
...
9038 / 94 = 96.148936170213 (the remainder is 14, so 94 is not a divisor of 9038)
9038 / 95 = 95.136842105263 (the remainder is 13, so 95 is not a divisor of 9038)