What are the divisors of 5423?

1, 11, 17, 29, 187, 319, 493, 5423

There is a total of 8 positive divisors.
The sum of these divisors is 6480.
The arithmetic mean is 810.

8 odd divisors

1, 11, 17, 29, 187, 319, 493, 5423

How to compute the divisors of 5423?

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 5423 by each of the numbers from 1 to 5423 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)

5423 / 1 = 5423 (the remainder is 0, so 1 is a divisor of 5423)
5423 / 2 = 2711.5 (the remainder is 1, so 2 is not a divisor of 5423)
5423 / 3 = 1807.6666666667 (the remainder is 2, so 3 is not a divisor of 5423)
...
5423 / 5422 = 1.0001844337883 (the remainder is 1, so 5422 is not a divisor of 5423)
5423 / 5423 = 1 (the remainder is 0, so 5423 is a divisor of 5423)

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 5423 (i.e. 73.641021177059). 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 $\frac{N}{d} = D$ )

5423 / 1 = 5423 (the remainder is 0, so 1 and 5423 are divisors of 5423)
5423 / 2 = 2711.5 (the remainder is 1, so 2 is not a divisor of 5423)
5423 / 3 = 1807.6666666667 (the remainder is 2, so 3 is not a divisor of 5423)
...
5423 / 72 = 75.319444444444 (the remainder is 23, so 72 is not a divisor of 5423)
5423 / 73 = 74.287671232877 (the remainder is 21, so 73 is not a divisor of 5423)