What are the divisors of 5610?

1, 2, 3, 5, 6, 10, 11, 15, 17, 22, 30, 33, 34, 51, 55, 66, 85, 102, 110, 165, 170, 187, 255, 330, 374, 510, 561, 935, 1122, 1870, 2805, 5610

There is a total of 32 positive divisors.
The sum of these divisors is 15552.
The arithmetic mean is 486.

16 even divisors

2, 6, 10, 22, 30, 34, 66, 102, 110, 170, 330, 374, 510, 1122, 1870, 5610

16 odd divisors

1, 3, 5, 11, 15, 17, 33, 51, 55, 85, 165, 187, 255, 561, 935, 2805

How to compute the divisors of 5610?

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 5610 by each of the numbers from 1 to 5610 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)

5610 / 1 = 5610 (the remainder is 0, so 1 is a divisor of 5610)
5610 / 2 = 2805 (the remainder is 0, so 2 is a divisor of 5610)
5610 / 3 = 1870 (the remainder is 0, so 3 is a divisor of 5610)
...
5610 / 5609 = 1.0001782848993 (the remainder is 1, so 5609 is not a divisor of 5610)
5610 / 5610 = 1 (the remainder is 0, so 5610 is a divisor of 5610)

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 5610 (i.e. 74.899933244296). 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 $\frac{N}{d} = D$ )

5610 / 1 = 5610 (the remainder is 0, so 1 and 5610 are divisors of 5610)
5610 / 2 = 2805 (the remainder is 0, so 2 and 2805 are divisors of 5610)
5610 / 3 = 1870 (the remainder is 0, so 3 and 1870 are divisors of 5610)
...
5610 / 73 = 76.849315068493 (the remainder is 62, so 73 is not a divisor of 5610)
5610 / 74 = 75.810810810811 (the remainder is 60, so 74 is not a divisor of 5610)