What are the divisors of 5665?

1, 5, 11, 55, 103, 515, 1133, 5665

There is a total of 8 positive divisors.
The sum of these divisors is 7488.
The arithmetic mean is 936.

8 odd divisors

1, 5, 11, 55, 103, 515, 1133, 5665

How to compute the divisors of 5665?

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 5665 by each of the numbers from 1 to 5665 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)

5665 / 1 = 5665 (the remainder is 0, so 1 is a divisor of 5665)
5665 / 2 = 2832.5 (the remainder is 1, so 2 is not a divisor of 5665)
5665 / 3 = 1888.3333333333 (the remainder is 1, so 3 is not a divisor of 5665)
...
5665 / 5664 = 1.0001765536723 (the remainder is 1, so 5664 is not a divisor of 5665)
5665 / 5665 = 1 (the remainder is 0, so 5665 is a divisor of 5665)

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 5665 (i.e. 75.266194270735). 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 $\frac{N}{d} = D$ )

5665 / 1 = 5665 (the remainder is 0, so 1 and 5665 are divisors of 5665)
5665 / 2 = 2832.5 (the remainder is 1, so 2 is not a divisor of 5665)
5665 / 3 = 1888.3333333333 (the remainder is 1, so 3 is not a divisor of 5665)
...
5665 / 74 = 76.554054054054 (the remainder is 41, so 74 is not a divisor of 5665)
5665 / 75 = 75.533333333333 (the remainder is 40, so 75 is not a divisor of 5665)