What are the divisors of 5381?

1, 5381

There is a total of 2 positive divisors.
The sum of these divisors is 5382.
The arithmetic mean is 2691.

2 odd divisors

1, 5381

How to compute the divisors of 5381?

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 5381 by each of the numbers from 1 to 5381 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)

5381 / 1 = 5381 (the remainder is 0, so 1 is a divisor of 5381)
5381 / 2 = 2690.5 (the remainder is 1, so 2 is not a divisor of 5381)
5381 / 3 = 1793.6666666667 (the remainder is 2, so 3 is not a divisor of 5381)
...
5381 / 5380 = 1.0001858736059 (the remainder is 1, so 5380 is not a divisor of 5381)
5381 / 5381 = 1 (the remainder is 0, so 5381 is a divisor of 5381)

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 5381 (i.e. 73.355299740373). 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 $\frac{N}{d} = D$ )

5381 / 1 = 5381 (the remainder is 0, so 1 and 5381 are divisors of 5381)
5381 / 2 = 2690.5 (the remainder is 1, so 2 is not a divisor of 5381)
5381 / 3 = 1793.6666666667 (the remainder is 2, so 3 is not a divisor of 5381)
...
5381 / 72 = 74.736111111111 (the remainder is 53, so 72 is not a divisor of 5381)
5381 / 73 = 73.712328767123 (the remainder is 52, so 73 is not a divisor of 5381)