What are the divisors of 5034?

1, 2, 3, 6, 839, 1678, 2517, 5034

There is a total of 8 positive divisors.
The sum of these divisors is 10080.
The arithmetic mean is 1260.

4 even divisors

2, 6, 1678, 5034

4 odd divisors

1, 3, 839, 2517

How to compute the divisors of 5034?

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 5034 by each of the numbers from 1 to 5034 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)

5034 / 1 = 5034 (the remainder is 0, so 1 is a divisor of 5034)
5034 / 2 = 2517 (the remainder is 0, so 2 is a divisor of 5034)
5034 / 3 = 1678 (the remainder is 0, so 3 is a divisor of 5034)
...
5034 / 5033 = 1.0001986886549 (the remainder is 1, so 5033 is not a divisor of 5034)
5034 / 5034 = 1 (the remainder is 0, so 5034 is a divisor of 5034)

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 5034 (i.e. 70.950687100267). 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 $\frac{N}{d} = D$ )

5034 / 1 = 5034 (the remainder is 0, so 1 and 5034 are divisors of 5034)
5034 / 2 = 2517 (the remainder is 0, so 2 and 2517 are divisors of 5034)
5034 / 3 = 1678 (the remainder is 0, so 3 and 1678 are divisors of 5034)
...
5034 / 69 = 72.95652173913 (the remainder is 66, so 69 is not a divisor of 5034)
5034 / 70 = 71.914285714286 (the remainder is 64, so 70 is not a divisor of 5034)