What are the divisors of 5633?

1, 43, 131, 5633

There is a total of 4 positive divisors.
The sum of these divisors is 5808.
The arithmetic mean is 1452.

4 odd divisors

1, 43, 131, 5633

How to compute the divisors of 5633?

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 5633 by each of the numbers from 1 to 5633 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)

5633 / 1 = 5633 (the remainder is 0, so 1 is a divisor of 5633)
5633 / 2 = 2816.5 (the remainder is 1, so 2 is not a divisor of 5633)
5633 / 3 = 1877.6666666667 (the remainder is 2, so 3 is not a divisor of 5633)
...
5633 / 5632 = 1.0001775568182 (the remainder is 1, so 5632 is not a divisor of 5633)
5633 / 5633 = 1 (the remainder is 0, so 5633 is a divisor of 5633)

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 5633 (i.e. 75.053314383843). 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 $\frac{N}{d} = D$ )

5633 / 1 = 5633 (the remainder is 0, so 1 and 5633 are divisors of 5633)
5633 / 2 = 2816.5 (the remainder is 1, so 2 is not a divisor of 5633)
5633 / 3 = 1877.6666666667 (the remainder is 2, so 3 is not a divisor of 5633)
...
5633 / 74 = 76.121621621622 (the remainder is 9, so 74 is not a divisor of 5633)
5633 / 75 = 75.106666666667 (the remainder is 8, so 75 is not a divisor of 5633)