What are the divisors of 6036?

1, 2, 3, 4, 6, 12, 503, 1006, 1509, 2012, 3018, 6036

There is a total of 12 positive divisors.
The sum of these divisors is 14112.
The arithmetic mean is 1176.

8 even divisors

2, 4, 6, 12, 1006, 2012, 3018, 6036

4 odd divisors

1, 3, 503, 1509

How to compute the divisors of 6036?

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 6036 by each of the numbers from 1 to 6036 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)

6036 / 1 = 6036 (the remainder is 0, so 1 is a divisor of 6036)
6036 / 2 = 3018 (the remainder is 0, so 2 is a divisor of 6036)
6036 / 3 = 2012 (the remainder is 0, so 3 is a divisor of 6036)
...
6036 / 6035 = 1.0001657000829 (the remainder is 1, so 6035 is not a divisor of 6036)
6036 / 6036 = 1 (the remainder is 0, so 6036 is a divisor of 6036)

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 6036 (i.e. 77.69169839822). 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 $\frac{N}{d} = D$ )

6036 / 1 = 6036 (the remainder is 0, so 1 and 6036 are divisors of 6036)
6036 / 2 = 3018 (the remainder is 0, so 2 and 3018 are divisors of 6036)
6036 / 3 = 2012 (the remainder is 0, so 3 and 2012 are divisors of 6036)
...
6036 / 76 = 79.421052631579 (the remainder is 32, so 76 is not a divisor of 6036)
6036 / 77 = 78.38961038961 (the remainder is 30, so 77 is not a divisor of 6036)