What are the divisors of 5611?

1, 31, 181, 5611

There is a total of 4 positive divisors.
The sum of these divisors is 5824.
The arithmetic mean is 1456.

4 odd divisors

1, 31, 181, 5611

How to compute the divisors of 5611?

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 5611 by each of the numbers from 1 to 5611 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)

5611 / 1 = 5611 (the remainder is 0, so 1 is a divisor of 5611)
5611 / 2 = 2805.5 (the remainder is 1, so 2 is not a divisor of 5611)
5611 / 3 = 1870.3333333333 (the remainder is 1, so 3 is not a divisor of 5611)
...
5611 / 5610 = 1.0001782531194 (the remainder is 1, so 5610 is not a divisor of 5611)
5611 / 5611 = 1 (the remainder is 0, so 5611 is a divisor of 5611)

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 5611 (i.e. 74.90660852021). 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 $\frac{N}{d} = D$ )

5611 / 1 = 5611 (the remainder is 0, so 1 and 5611 are divisors of 5611)
5611 / 2 = 2805.5 (the remainder is 1, so 2 is not a divisor of 5611)
5611 / 3 = 1870.3333333333 (the remainder is 1, so 3 is not a divisor of 5611)
...
5611 / 73 = 76.86301369863 (the remainder is 63, so 73 is not a divisor of 5611)
5611 / 74 = 75.824324324324 (the remainder is 61, so 74 is not a divisor of 5611)