What are the divisors of 5038?

1, 2, 11, 22, 229, 458, 2519, 5038

There is a total of 8 positive divisors.
The sum of these divisors is 8280.
The arithmetic mean is 1035.

4 even divisors

2, 22, 458, 5038

4 odd divisors

1, 11, 229, 2519

How to compute the divisors of 5038?

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 5038 by each of the numbers from 1 to 5038 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)

5038 / 1 = 5038 (the remainder is 0, so 1 is a divisor of 5038)
5038 / 2 = 2519 (the remainder is 0, so 2 is a divisor of 5038)
5038 / 3 = 1679.3333333333 (the remainder is 1, so 3 is not a divisor of 5038)
...
5038 / 5037 = 1.0001985308716 (the remainder is 1, so 5037 is not a divisor of 5038)
5038 / 5038 = 1 (the remainder is 0, so 5038 is a divisor of 5038)

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 5038 (i.e. 70.978870095261). 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 $\frac{N}{d} = D$ )

5038 / 1 = 5038 (the remainder is 0, so 1 and 5038 are divisors of 5038)
5038 / 2 = 2519 (the remainder is 0, so 2 and 2519 are divisors of 5038)
5038 / 3 = 1679.3333333333 (the remainder is 1, so 3 is not a divisor of 5038)
...
5038 / 69 = 73.014492753623 (the remainder is 1, so 69 is not a divisor of 5038)
5038 / 70 = 71.971428571429 (the remainder is 68, so 70 is not a divisor of 5038)