What are the divisors of 5343?

1, 3, 13, 39, 137, 411, 1781, 5343

There is a total of 8 positive divisors.
The sum of these divisors is 7728.
The arithmetic mean is 966.

8 odd divisors

1, 3, 13, 39, 137, 411, 1781, 5343

How to compute the divisors of 5343?

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 5343 by each of the numbers from 1 to 5343 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)

5343 / 1 = 5343 (the remainder is 0, so 1 is a divisor of 5343)
5343 / 2 = 2671.5 (the remainder is 1, so 2 is not a divisor of 5343)
5343 / 3 = 1781 (the remainder is 0, so 3 is a divisor of 5343)
...
5343 / 5342 = 1.0001871958068 (the remainder is 1, so 5342 is not a divisor of 5343)
5343 / 5343 = 1 (the remainder is 0, so 5343 is a divisor of 5343)

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 5343 (i.e. 73.095827514298). 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 $\frac{N}{d} = D$ )

5343 / 1 = 5343 (the remainder is 0, so 1 and 5343 are divisors of 5343)
5343 / 2 = 2671.5 (the remainder is 1, so 2 is not a divisor of 5343)
5343 / 3 = 1781 (the remainder is 0, so 3 and 1781 are divisors of 5343)
...
5343 / 72 = 74.208333333333 (the remainder is 15, so 72 is not a divisor of 5343)
5343 / 73 = 73.191780821918 (the remainder is 14, so 73 is not a divisor of 5343)