What are the divisors of 5643?

1, 3, 9, 11, 19, 27, 33, 57, 99, 171, 209, 297, 513, 627, 1881, 5643

There is a total of 16 positive divisors.
The sum of these divisors is 9600.
The arithmetic mean is 600.

16 odd divisors

1, 3, 9, 11, 19, 27, 33, 57, 99, 171, 209, 297, 513, 627, 1881, 5643

How to compute the divisors of 5643?

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 5643 by each of the numbers from 1 to 5643 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)

5643 / 1 = 5643 (the remainder is 0, so 1 is a divisor of 5643)
5643 / 2 = 2821.5 (the remainder is 1, so 2 is not a divisor of 5643)
5643 / 3 = 1881 (the remainder is 0, so 3 is a divisor of 5643)
...
5643 / 5642 = 1.0001772421127 (the remainder is 1, so 5642 is not a divisor of 5643)
5643 / 5643 = 1 (the remainder is 0, so 5643 is a divisor of 5643)

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 5643 (i.e. 75.119904153293). 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 $\frac{N}{d} = D$ )

5643 / 1 = 5643 (the remainder is 0, so 1 and 5643 are divisors of 5643)
5643 / 2 = 2821.5 (the remainder is 1, so 2 is not a divisor of 5643)
5643 / 3 = 1881 (the remainder is 0, so 3 and 1881 are divisors of 5643)
...
5643 / 74 = 76.256756756757 (the remainder is 19, so 74 is not a divisor of 5643)
5643 / 75 = 75.24 (the remainder is 18, so 75 is not a divisor of 5643)