What are the divisors of 5511?

1, 3, 11, 33, 167, 501, 1837, 5511

There is a total of 8 positive divisors.
The sum of these divisors is 8064.
The arithmetic mean is 1008.

8 odd divisors

1, 3, 11, 33, 167, 501, 1837, 5511

How to compute the divisors of 5511?

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 5511 by each of the numbers from 1 to 5511 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)

5511 / 1 = 5511 (the remainder is 0, so 1 is a divisor of 5511)
5511 / 2 = 2755.5 (the remainder is 1, so 2 is not a divisor of 5511)
5511 / 3 = 1837 (the remainder is 0, so 3 is a divisor of 5511)
...
5511 / 5510 = 1.0001814882033 (the remainder is 1, so 5510 is not a divisor of 5511)
5511 / 5511 = 1 (the remainder is 0, so 5511 is a divisor of 5511)

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 5511 (i.e. 74.23610981187). 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 $\frac{N}{d} = D$ )

5511 / 1 = 5511 (the remainder is 0, so 1 and 5511 are divisors of 5511)
5511 / 2 = 2755.5 (the remainder is 1, so 2 is not a divisor of 5511)
5511 / 3 = 1837 (the remainder is 0, so 3 and 1837 are divisors of 5511)
...
5511 / 73 = 75.493150684932 (the remainder is 36, so 73 is not a divisor of 5511)
5511 / 74 = 74.472972972973 (the remainder is 35, so 74 is not a divisor of 5511)