What are the divisors of 5036?

1, 2, 4, 1259, 2518, 5036

There is a total of 6 positive divisors.
The sum of these divisors is 8820.
The arithmetic mean is 1470.

4 even divisors

2, 4, 2518, 5036

2 odd divisors

1, 1259

How to compute the divisors of 5036?

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 5036 by each of the numbers from 1 to 5036 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)

5036 / 1 = 5036 (the remainder is 0, so 1 is a divisor of 5036)
5036 / 2 = 2518 (the remainder is 0, so 2 is a divisor of 5036)
5036 / 3 = 1678.6666666667 (the remainder is 2, so 3 is not a divisor of 5036)
...
5036 / 5035 = 1.0001986097319 (the remainder is 1, so 5035 is not a divisor of 5036)
5036 / 5036 = 1 (the remainder is 0, so 5036 is a divisor of 5036)

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 5036 (i.e. 70.964779996841). 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 $\frac{N}{d} = D$ )

5036 / 1 = 5036 (the remainder is 0, so 1 and 5036 are divisors of 5036)
5036 / 2 = 2518 (the remainder is 0, so 2 and 2518 are divisors of 5036)
5036 / 3 = 1678.6666666667 (the remainder is 2, so 3 is not a divisor of 5036)
...
5036 / 69 = 72.985507246377 (the remainder is 68, so 69 is not a divisor of 5036)
5036 / 70 = 71.942857142857 (the remainder is 66, so 70 is not a divisor of 5036)