What are the divisors of 4036?

1, 2, 4, 1009, 2018, 4036

There is a total of 6 positive divisors.
The sum of these divisors is 7070.
The arithmetic mean is 1178.3333333333.

4 even divisors

2, 4, 2018, 4036

2 odd divisors

1, 1009

How to compute the divisors of 4036?

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 4036 by each of the numbers from 1 to 4036 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)

4036 / 1 = 4036 (the remainder is 0, so 1 is a divisor of 4036)
4036 / 2 = 2018 (the remainder is 0, so 2 is a divisor of 4036)
4036 / 3 = 1345.3333333333 (the remainder is 1, so 3 is not a divisor of 4036)
...
4036 / 4035 = 1.0002478314746 (the remainder is 1, so 4035 is not a divisor of 4036)
4036 / 4036 = 1 (the remainder is 0, so 4036 is a divisor of 4036)

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 4036 (i.e. 63.529520697074). 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 $\frac{N}{d} = D$ )

4036 / 1 = 4036 (the remainder is 0, so 1 and 4036 are divisors of 4036)
4036 / 2 = 2018 (the remainder is 0, so 2 and 2018 are divisors of 4036)
4036 / 3 = 1345.3333333333 (the remainder is 1, so 3 is not a divisor of 4036)
...
4036 / 62 = 65.096774193548 (the remainder is 6, so 62 is not a divisor of 4036)
4036 / 63 = 64.063492063492 (the remainder is 4, so 63 is not a divisor of 4036)