What are the divisors of 5500?

1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 125, 220, 250, 275, 500, 550, 1100, 1375, 2750, 5500

There is a total of 24 positive divisors.
The sum of these divisors is 13104.
The arithmetic mean is 546.

16 even divisors

2, 4, 10, 20, 22, 44, 50, 100, 110, 220, 250, 500, 550, 1100, 2750, 5500

8 odd divisors

1, 5, 11, 25, 55, 125, 275, 1375

How to compute the divisors of 5500?

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 5500 by each of the numbers from 1 to 5500 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)

5500 / 1 = 5500 (the remainder is 0, so 1 is a divisor of 5500)
5500 / 2 = 2750 (the remainder is 0, so 2 is a divisor of 5500)
5500 / 3 = 1833.3333333333 (the remainder is 1, so 3 is not a divisor of 5500)
...
5500 / 5499 = 1.0001818512457 (the remainder is 1, so 5499 is not a divisor of 5500)
5500 / 5500 = 1 (the remainder is 0, so 5500 is a divisor of 5500)

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 5500 (i.e. 74.161984870957). 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 $\frac{N}{d} = D$ )

5500 / 1 = 5500 (the remainder is 0, so 1 and 5500 are divisors of 5500)
5500 / 2 = 2750 (the remainder is 0, so 2 and 2750 are divisors of 5500)
5500 / 3 = 1833.3333333333 (the remainder is 1, so 3 is not a divisor of 5500)
...
5500 / 73 = 75.342465753425 (the remainder is 25, so 73 is not a divisor of 5500)
5500 / 74 = 74.324324324324 (the remainder is 24, so 74 is not a divisor of 5500)