What are the divisors of 5663?

1, 7, 809, 5663

There is a total of 4 positive divisors.
The sum of these divisors is 6480.
The arithmetic mean is 1620.

4 odd divisors

1, 7, 809, 5663

How to compute the divisors of 5663?

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 5663 by each of the numbers from 1 to 5663 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)

5663 / 1 = 5663 (the remainder is 0, so 1 is a divisor of 5663)
5663 / 2 = 2831.5 (the remainder is 1, so 2 is not a divisor of 5663)
5663 / 3 = 1887.6666666667 (the remainder is 2, so 3 is not a divisor of 5663)
...
5663 / 5662 = 1.0001766160367 (the remainder is 1, so 5662 is not a divisor of 5663)
5663 / 5663 = 1 (the remainder is 0, so 5663 is a divisor of 5663)

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 5663 (i.e. 75.252906920597). 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 $\frac{N}{d} = D$ )

5663 / 1 = 5663 (the remainder is 0, so 1 and 5663 are divisors of 5663)
5663 / 2 = 2831.5 (the remainder is 1, so 2 is not a divisor of 5663)
5663 / 3 = 1887.6666666667 (the remainder is 2, so 3 is not a divisor of 5663)
...
5663 / 74 = 76.527027027027 (the remainder is 39, so 74 is not a divisor of 5663)
5663 / 75 = 75.506666666667 (the remainder is 38, so 75 is not a divisor of 5663)