What are the divisors of 5596?

1, 2, 4, 1399, 2798, 5596

There is a total of 6 positive divisors.
The sum of these divisors is 9800.
The arithmetic mean is 1633.3333333333.

4 even divisors

2, 4, 2798, 5596

2 odd divisors

1, 1399

How to compute the divisors of 5596?

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 5596 by each of the numbers from 1 to 5596 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)

5596 / 1 = 5596 (the remainder is 0, so 1 is a divisor of 5596)
5596 / 2 = 2798 (the remainder is 0, so 2 is a divisor of 5596)
5596 / 3 = 1865.3333333333 (the remainder is 1, so 3 is not a divisor of 5596)
...
5596 / 5595 = 1.0001787310098 (the remainder is 1, so 5595 is not a divisor of 5596)
5596 / 5596 = 1 (the remainder is 0, so 5596 is a divisor of 5596)

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 5596 (i.e. 74.80641683706). 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 $\frac{N}{d} = D$ )

5596 / 1 = 5596 (the remainder is 0, so 1 and 5596 are divisors of 5596)
5596 / 2 = 2798 (the remainder is 0, so 2 and 2798 are divisors of 5596)
5596 / 3 = 1865.3333333333 (the remainder is 1, so 3 is not a divisor of 5596)
...
5596 / 73 = 76.657534246575 (the remainder is 48, so 73 is not a divisor of 5596)
5596 / 74 = 75.621621621622 (the remainder is 46, so 74 is not a divisor of 5596)