What are the divisors of 5613?

1, 3, 1871, 5613

There is a total of 4 positive divisors.
The sum of these divisors is 7488.
The arithmetic mean is 1872.

4 odd divisors

1, 3, 1871, 5613

How to compute the divisors of 5613?

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 5613 by each of the numbers from 1 to 5613 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)

5613 / 1 = 5613 (the remainder is 0, so 1 is a divisor of 5613)
5613 / 2 = 2806.5 (the remainder is 1, so 2 is not a divisor of 5613)
5613 / 3 = 1871 (the remainder is 0, so 3 is a divisor of 5613)
...
5613 / 5612 = 1.0001781895937 (the remainder is 1, so 5612 is not a divisor of 5613)
5613 / 5613 = 1 (the remainder is 0, so 5613 is a divisor of 5613)

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 5613 (i.e. 74.919957287761). 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 $\frac{N}{d} = D$ )

5613 / 1 = 5613 (the remainder is 0, so 1 and 5613 are divisors of 5613)
5613 / 2 = 2806.5 (the remainder is 1, so 2 is not a divisor of 5613)
5613 / 3 = 1871 (the remainder is 0, so 3 and 1871 are divisors of 5613)
...
5613 / 73 = 76.890410958904 (the remainder is 65, so 73 is not a divisor of 5613)
5613 / 74 = 75.851351351351 (the remainder is 63, so 74 is not a divisor of 5613)