What are the divisors of 5580?

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 31, 36, 45, 60, 62, 90, 93, 124, 155, 180, 186, 279, 310, 372, 465, 558, 620, 930, 1116, 1395, 1860, 2790, 5580

There is a total of 36 positive divisors.
The sum of these divisors is 17472.
The arithmetic mean is 485.33333333333.

24 even divisors

2, 4, 6, 10, 12, 18, 20, 30, 36, 60, 62, 90, 124, 180, 186, 310, 372, 558, 620, 930, 1116, 1860, 2790, 5580

12 odd divisors

1, 3, 5, 9, 15, 31, 45, 93, 155, 279, 465, 1395

How to compute the divisors of 5580?

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 5580 by each of the numbers from 1 to 5580 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)

5580 / 1 = 5580 (the remainder is 0, so 1 is a divisor of 5580)
5580 / 2 = 2790 (the remainder is 0, so 2 is a divisor of 5580)
5580 / 3 = 1860 (the remainder is 0, so 3 is a divisor of 5580)
...
5580 / 5579 = 1.000179243592 (the remainder is 1, so 5579 is not a divisor of 5580)
5580 / 5580 = 1 (the remainder is 0, so 5580 is a divisor of 5580)

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 5580 (i.e. 74.699397587932). 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 $\frac{N}{d} = D$ )

5580 / 1 = 5580 (the remainder is 0, so 1 and 5580 are divisors of 5580)
5580 / 2 = 2790 (the remainder is 0, so 2 and 2790 are divisors of 5580)
5580 / 3 = 1860 (the remainder is 0, so 3 and 1860 are divisors of 5580)
...
5580 / 73 = 76.438356164384 (the remainder is 32, so 73 is not a divisor of 5580)
5580 / 74 = 75.405405405405 (the remainder is 30, so 74 is not a divisor of 5580)