What are the divisors of 5622?

1, 2, 3, 6, 937, 1874, 2811, 5622

There is a total of 8 positive divisors.
The sum of these divisors is 11256.
The arithmetic mean is 1407.

4 even divisors

2, 6, 1874, 5622

4 odd divisors

1, 3, 937, 2811

How to compute the divisors of 5622?

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 5622 by each of the numbers from 1 to 5622 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)

5622 / 1 = 5622 (the remainder is 0, so 1 is a divisor of 5622)
5622 / 2 = 2811 (the remainder is 0, so 2 is a divisor of 5622)
5622 / 3 = 1874 (the remainder is 0, so 3 is a divisor of 5622)
...
5622 / 5621 = 1.0001779042875 (the remainder is 1, so 5621 is not a divisor of 5622)
5622 / 5622 = 1 (the remainder is 0, so 5622 is a divisor of 5622)

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 5622 (i.e. 74.979997332622). 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 $\frac{N}{d} = D$ )

5622 / 1 = 5622 (the remainder is 0, so 1 and 5622 are divisors of 5622)
5622 / 2 = 2811 (the remainder is 0, so 2 and 2811 are divisors of 5622)
5622 / 3 = 1874 (the remainder is 0, so 3 and 1874 are divisors of 5622)
...
5622 / 73 = 77.013698630137 (the remainder is 1, so 73 is not a divisor of 5622)
5622 / 74 = 75.972972972973 (the remainder is 72, so 74 is not a divisor of 5622)