What are the divisors of 5561?

1, 67, 83, 5561

There is a total of 4 positive divisors.
The sum of these divisors is 5712.
The arithmetic mean is 1428.

4 odd divisors

1, 67, 83, 5561

How to compute the divisors of 5561?

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 5561 by each of the numbers from 1 to 5561 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)

5561 / 1 = 5561 (the remainder is 0, so 1 is a divisor of 5561)
5561 / 2 = 2780.5 (the remainder is 1, so 2 is not a divisor of 5561)
5561 / 3 = 1853.6666666667 (the remainder is 2, so 3 is not a divisor of 5561)
...
5561 / 5560 = 1.0001798561151 (the remainder is 1, so 5560 is not a divisor of 5561)
5561 / 5561 = 1 (the remainder is 0, so 5561 is a divisor of 5561)

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 5561 (i.e. 74.572112750009). 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 $\frac{N}{d} = D$ )

5561 / 1 = 5561 (the remainder is 0, so 1 and 5561 are divisors of 5561)
5561 / 2 = 2780.5 (the remainder is 1, so 2 is not a divisor of 5561)
5561 / 3 = 1853.6666666667 (the remainder is 2, so 3 is not a divisor of 5561)
...
5561 / 73 = 76.178082191781 (the remainder is 13, so 73 is not a divisor of 5561)
5561 / 74 = 75.148648648649 (the remainder is 11, so 74 is not a divisor of 5561)