What are the divisors of 5323?

1, 5323

There is a total of 2 positive divisors.
The sum of these divisors is 5324.
The arithmetic mean is 2662.

2 odd divisors

1, 5323

How to compute the divisors of 5323?

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 5323 by each of the numbers from 1 to 5323 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)

5323 / 1 = 5323 (the remainder is 0, so 1 is a divisor of 5323)
5323 / 2 = 2661.5 (the remainder is 1, so 2 is not a divisor of 5323)
5323 / 3 = 1774.3333333333 (the remainder is 1, so 3 is not a divisor of 5323)
...
5323 / 5322 = 1.000187899286 (the remainder is 1, so 5322 is not a divisor of 5323)
5323 / 5323 = 1 (the remainder is 0, so 5323 is a divisor of 5323)

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 5323 (i.e. 72.958892535455). 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 $\frac{N}{d} = D$ )

5323 / 1 = 5323 (the remainder is 0, so 1 and 5323 are divisors of 5323)
5323 / 2 = 2661.5 (the remainder is 1, so 2 is not a divisor of 5323)
5323 / 3 = 1774.3333333333 (the remainder is 1, so 3 is not a divisor of 5323)
...
5323 / 71 = 74.971830985915 (the remainder is 69, so 71 is not a divisor of 5323)
5323 / 72 = 73.930555555556 (the remainder is 67, so 72 is not a divisor of 5323)