What are the divisors of 2036?

1, 2, 4, 509, 1018, 2036

There is a total of 6 positive divisors.
The sum of these divisors is 3570.
The arithmetic mean is 595.

4 even divisors

2, 4, 1018, 2036

2 odd divisors

1, 509

How to compute the divisors of 2036?

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 2036 by each of the numbers from 1 to 2036 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)

2036 / 1 = 2036 (the remainder is 0, so 1 is a divisor of 2036)
2036 / 2 = 1018 (the remainder is 0, so 2 is a divisor of 2036)
2036 / 3 = 678.66666666667 (the remainder is 2, so 3 is not a divisor of 2036)
...
2036 / 2035 = 1.0004914004914 (the remainder is 1, so 2035 is not a divisor of 2036)
2036 / 2036 = 1 (the remainder is 0, so 2036 is a divisor of 2036)

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 2036 (i.e. 45.122056690714). 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 $\frac{N}{d} = D$ )

2036 / 1 = 2036 (the remainder is 0, so 1 and 2036 are divisors of 2036)
2036 / 2 = 1018 (the remainder is 0, so 2 and 1018 are divisors of 2036)
2036 / 3 = 678.66666666667 (the remainder is 2, so 3 is not a divisor of 2036)
...
2036 / 44 = 46.272727272727 (the remainder is 12, so 44 is not a divisor of 2036)
2036 / 45 = 45.244444444444 (the remainder is 11, so 45 is not a divisor of 2036)