What are the divisors of 5385?

1, 3, 5, 15, 359, 1077, 1795, 5385

There is a total of 8 positive divisors.
The sum of these divisors is 8640.
The arithmetic mean is 1080.

8 odd divisors

1, 3, 5, 15, 359, 1077, 1795, 5385

How to compute the divisors of 5385?

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 5385 by each of the numbers from 1 to 5385 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)

5385 / 1 = 5385 (the remainder is 0, so 1 is a divisor of 5385)
5385 / 2 = 2692.5 (the remainder is 1, so 2 is not a divisor of 5385)
5385 / 3 = 1795 (the remainder is 0, so 3 is a divisor of 5385)
...
5385 / 5384 = 1.0001857355126 (the remainder is 1, so 5384 is not a divisor of 5385)
5385 / 5385 = 1 (the remainder is 0, so 5385 is a divisor of 5385)

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 5385 (i.e. 73.382559235829). 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 $\frac{N}{d} = D$ )

5385 / 1 = 5385 (the remainder is 0, so 1 and 5385 are divisors of 5385)
5385 / 2 = 2692.5 (the remainder is 1, so 2 is not a divisor of 5385)
5385 / 3 = 1795 (the remainder is 0, so 3 and 1795 are divisors of 5385)
...
5385 / 72 = 74.791666666667 (the remainder is 57, so 72 is not a divisor of 5385)
5385 / 73 = 73.767123287671 (the remainder is 56, so 73 is not a divisor of 5385)