What are the divisors of 5044?

1, 2, 4, 13, 26, 52, 97, 194, 388, 1261, 2522, 5044

There is a total of 12 positive divisors.
The sum of these divisors is 9604.
The arithmetic mean is 800.33333333333.

8 even divisors

2, 4, 26, 52, 194, 388, 2522, 5044

4 odd divisors

1, 13, 97, 1261

How to compute the divisors of 5044?

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 5044 by each of the numbers from 1 to 5044 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)

5044 / 1 = 5044 (the remainder is 0, so 1 is a divisor of 5044)
5044 / 2 = 2522 (the remainder is 0, so 2 is a divisor of 5044)
5044 / 3 = 1681.3333333333 (the remainder is 1, so 3 is not a divisor of 5044)
...
5044 / 5043 = 1.0001982946659 (the remainder is 1, so 5043 is not a divisor of 5044)
5044 / 5044 = 1 (the remainder is 0, so 5044 is a divisor of 5044)

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 5044 (i.e. 71.021123618259). 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 $\frac{N}{d} = D$ )

5044 / 1 = 5044 (the remainder is 0, so 1 and 5044 are divisors of 5044)
5044 / 2 = 2522 (the remainder is 0, so 2 and 2522 are divisors of 5044)
5044 / 3 = 1681.3333333333 (the remainder is 1, so 3 is not a divisor of 5044)
...
5044 / 70 = 72.057142857143 (the remainder is 4, so 70 is not a divisor of 5044)
5044 / 71 = 71.042253521127 (the remainder is 3, so 71 is not a divisor of 5044)