What are the divisors of 5337?

1, 3, 9, 593, 1779, 5337

There is a total of 6 positive divisors.
The sum of these divisors is 7722.
The arithmetic mean is 1287.

6 odd divisors

1, 3, 9, 593, 1779, 5337

How to compute the divisors of 5337?

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 5337 by each of the numbers from 1 to 5337 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)

5337 / 1 = 5337 (the remainder is 0, so 1 is a divisor of 5337)
5337 / 2 = 2668.5 (the remainder is 1, so 2 is not a divisor of 5337)
5337 / 3 = 1779 (the remainder is 0, so 3 is a divisor of 5337)
...
5337 / 5336 = 1.0001874062969 (the remainder is 1, so 5336 is not a divisor of 5337)
5337 / 5337 = 1 (the remainder is 0, so 5337 is a divisor of 5337)

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 5337 (i.e. 73.054773971316). 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 $\frac{N}{d} = D$ )

5337 / 1 = 5337 (the remainder is 0, so 1 and 5337 are divisors of 5337)
5337 / 2 = 2668.5 (the remainder is 1, so 2 is not a divisor of 5337)
5337 / 3 = 1779 (the remainder is 0, so 3 and 1779 are divisors of 5337)
...
5337 / 72 = 74.125 (the remainder is 9, so 72 is not a divisor of 5337)
5337 / 73 = 73.109589041096 (the remainder is 8, so 73 is not a divisor of 5337)