What are the divisors of 5395?

1, 5, 13, 65, 83, 415, 1079, 5395

There is a total of 8 positive divisors.
The sum of these divisors is 7056.
The arithmetic mean is 882.

8 odd divisors

1, 5, 13, 65, 83, 415, 1079, 5395

How to compute the divisors of 5395?

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 5395 by each of the numbers from 1 to 5395 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)

5395 / 1 = 5395 (the remainder is 0, so 1 is a divisor of 5395)
5395 / 2 = 2697.5 (the remainder is 1, so 2 is not a divisor of 5395)
5395 / 3 = 1798.3333333333 (the remainder is 1, so 3 is not a divisor of 5395)
...
5395 / 5394 = 1.0001853911754 (the remainder is 1, so 5394 is not a divisor of 5395)
5395 / 5395 = 1 (the remainder is 0, so 5395 is a divisor of 5395)

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 5395 (i.e. 73.450663713815). 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 $\frac{N}{d} = D$ )

5395 / 1 = 5395 (the remainder is 0, so 1 and 5395 are divisors of 5395)
5395 / 2 = 2697.5 (the remainder is 1, so 2 is not a divisor of 5395)
5395 / 3 = 1798.3333333333 (the remainder is 1, so 3 is not a divisor of 5395)
...
5395 / 72 = 74.930555555556 (the remainder is 67, so 72 is not a divisor of 5395)
5395 / 73 = 73.904109589041 (the remainder is 66, so 73 is not a divisor of 5395)