What are the divisors of 5515?

1, 5, 1103, 5515

There is a total of 4 positive divisors.
The sum of these divisors is 6624.
The arithmetic mean is 1656.

4 odd divisors

1, 5, 1103, 5515

How to compute the divisors of 5515?

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 5515 by each of the numbers from 1 to 5515 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)

5515 / 1 = 5515 (the remainder is 0, so 1 is a divisor of 5515)
5515 / 2 = 2757.5 (the remainder is 1, so 2 is not a divisor of 5515)
5515 / 3 = 1838.3333333333 (the remainder is 1, so 3 is not a divisor of 5515)
...
5515 / 5514 = 1.000181356547 (the remainder is 1, so 5514 is not a divisor of 5515)
5515 / 5515 = 1 (the remainder is 0, so 5515 is a divisor of 5515)

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 5515 (i.e. 74.263045991933). 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 $\frac{N}{d} = D$ )

5515 / 1 = 5515 (the remainder is 0, so 1 and 5515 are divisors of 5515)
5515 / 2 = 2757.5 (the remainder is 1, so 2 is not a divisor of 5515)
5515 / 3 = 1838.3333333333 (the remainder is 1, so 3 is not a divisor of 5515)
...
5515 / 73 = 75.547945205479 (the remainder is 40, so 73 is not a divisor of 5515)
5515 / 74 = 74.527027027027 (the remainder is 39, so 74 is not a divisor of 5515)