What are the divisors of 5636?

1, 2, 4, 1409, 2818, 5636

There is a total of 6 positive divisors.
The sum of these divisors is 9870.
The arithmetic mean is 1645.

4 even divisors

2, 4, 2818, 5636

2 odd divisors

1, 1409

How to compute the divisors of 5636?

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 5636 by each of the numbers from 1 to 5636 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)

5636 / 1 = 5636 (the remainder is 0, so 1 is a divisor of 5636)
5636 / 2 = 2818 (the remainder is 0, so 2 is a divisor of 5636)
5636 / 3 = 1878.6666666667 (the remainder is 2, so 3 is not a divisor of 5636)
...
5636 / 5635 = 1.0001774622893 (the remainder is 1, so 5635 is not a divisor of 5636)
5636 / 5636 = 1 (the remainder is 0, so 5636 is a divisor of 5636)

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 5636 (i.e. 75.073297516494). 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 $\frac{N}{d} = D$ )

5636 / 1 = 5636 (the remainder is 0, so 1 and 5636 are divisors of 5636)
5636 / 2 = 2818 (the remainder is 0, so 2 and 2818 are divisors of 5636)
5636 / 3 = 1878.6666666667 (the remainder is 2, so 3 is not a divisor of 5636)
...
5636 / 74 = 76.162162162162 (the remainder is 12, so 74 is not a divisor of 5636)
5636 / 75 = 75.146666666667 (the remainder is 11, so 75 is not a divisor of 5636)