What are the divisors of 5327?

1, 7, 761, 5327

There is a total of 4 positive divisors.
The sum of these divisors is 6096.
The arithmetic mean is 1524.

4 odd divisors

1, 7, 761, 5327

How to compute the divisors of 5327?

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 5327 by each of the numbers from 1 to 5327 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)

5327 / 1 = 5327 (the remainder is 0, so 1 is a divisor of 5327)
5327 / 2 = 2663.5 (the remainder is 1, so 2 is not a divisor of 5327)
5327 / 3 = 1775.6666666667 (the remainder is 2, so 3 is not a divisor of 5327)
...
5327 / 5326 = 1.0001877581675 (the remainder is 1, so 5326 is not a divisor of 5327)
5327 / 5327 = 1 (the remainder is 0, so 5327 is a divisor of 5327)

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 5327 (i.e. 72.986300084331). 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 $\frac{N}{d} = D$ )

5327 / 1 = 5327 (the remainder is 0, so 1 and 5327 are divisors of 5327)
5327 / 2 = 2663.5 (the remainder is 1, so 2 is not a divisor of 5327)
5327 / 3 = 1775.6666666667 (the remainder is 2, so 3 is not a divisor of 5327)
...
5327 / 71 = 75.028169014085 (the remainder is 2, so 71 is not a divisor of 5327)
5327 / 72 = 73.986111111111 (the remainder is 71, so 72 is not a divisor of 5327)