What are the divisors of 5505?

1, 3, 5, 15, 367, 1101, 1835, 5505

There is a total of 8 positive divisors.
The sum of these divisors is 8832.
The arithmetic mean is 1104.

8 odd divisors

1, 3, 5, 15, 367, 1101, 1835, 5505

How to compute the divisors of 5505?

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 5505 by each of the numbers from 1 to 5505 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)

5505 / 1 = 5505 (the remainder is 0, so 1 is a divisor of 5505)
5505 / 2 = 2752.5 (the remainder is 1, so 2 is not a divisor of 5505)
5505 / 3 = 1835 (the remainder is 0, so 3 is a divisor of 5505)
...
5505 / 5504 = 1.0001816860465 (the remainder is 1, so 5504 is not a divisor of 5505)
5505 / 5505 = 1 (the remainder is 0, so 5505 is a divisor of 5505)

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 5505 (i.e. 74.195687206198). 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 $\frac{N}{d} = D$ )

5505 / 1 = 5505 (the remainder is 0, so 1 and 5505 are divisors of 5505)
5505 / 2 = 2752.5 (the remainder is 1, so 2 is not a divisor of 5505)
5505 / 3 = 1835 (the remainder is 0, so 3 and 1835 are divisors of 5505)
...
5505 / 73 = 75.41095890411 (the remainder is 30, so 73 is not a divisor of 5505)
5505 / 74 = 74.391891891892 (the remainder is 29, so 74 is not a divisor of 5505)