What are the divisors of 5653?

1, 5653

There is a total of 2 positive divisors.
The sum of these divisors is 5654.
The arithmetic mean is 2827.

2 odd divisors

1, 5653

How to compute the divisors of 5653?

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 5653 by each of the numbers from 1 to 5653 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)

5653 / 1 = 5653 (the remainder is 0, so 1 is a divisor of 5653)
5653 / 2 = 2826.5 (the remainder is 1, so 2 is not a divisor of 5653)
5653 / 3 = 1884.3333333333 (the remainder is 1, so 3 is not a divisor of 5653)
...
5653 / 5652 = 1.0001769285209 (the remainder is 1, so 5652 is not a divisor of 5653)
5653 / 5653 = 1 (the remainder is 0, so 5653 is a divisor of 5653)

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 5653 (i.e. 75.186434946738). 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 $\frac{N}{d} = D$ )

5653 / 1 = 5653 (the remainder is 0, so 1 and 5653 are divisors of 5653)
5653 / 2 = 2826.5 (the remainder is 1, so 2 is not a divisor of 5653)
5653 / 3 = 1884.3333333333 (the remainder is 1, so 3 is not a divisor of 5653)
...
5653 / 74 = 76.391891891892 (the remainder is 29, so 74 is not a divisor of 5653)
5653 / 75 = 75.373333333333 (the remainder is 28, so 75 is not a divisor of 5653)