What are the divisors of 9044?

1, 2, 4, 7, 14, 17, 19, 28, 34, 38, 68, 76, 119, 133, 238, 266, 323, 476, 532, 646, 1292, 2261, 4522, 9044

There is a total of 24 positive divisors.
The sum of these divisors is 20160.
The arithmetic mean is 840.

16 even divisors

2, 4, 14, 28, 34, 38, 68, 76, 238, 266, 476, 532, 646, 1292, 4522, 9044

8 odd divisors

1, 7, 17, 19, 119, 133, 323, 2261

How to compute the divisors of 9044?

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 9044 by each of the numbers from 1 to 9044 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)

9044 / 1 = 9044 (the remainder is 0, so 1 is a divisor of 9044)
9044 / 2 = 4522 (the remainder is 0, so 2 is a divisor of 9044)
9044 / 3 = 3014.6666666667 (the remainder is 2, so 3 is not a divisor of 9044)
...
9044 / 9043 = 1.0001105827712 (the remainder is 1, so 9043 is not a divisor of 9044)
9044 / 9044 = 1 (the remainder is 0, so 9044 is a divisor of 9044)

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 9044 (i.e. 95.09994742375). 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 $\frac{N}{d} = D$ )

9044 / 1 = 9044 (the remainder is 0, so 1 and 9044 are divisors of 9044)
9044 / 2 = 4522 (the remainder is 0, so 2 and 4522 are divisors of 9044)
9044 / 3 = 3014.6666666667 (the remainder is 2, so 3 is not a divisor of 9044)
...
9044 / 94 = 96.212765957447 (the remainder is 20, so 94 is not a divisor of 9044)
9044 / 95 = 95.2 (the remainder is 19, so 95 is not a divisor of 9044)