What are the divisors of 5379?

1, 3, 11, 33, 163, 489, 1793, 5379

There is a total of 8 positive divisors.
The sum of these divisors is 7872.
The arithmetic mean is 984.

8 odd divisors

1, 3, 11, 33, 163, 489, 1793, 5379

How to compute the divisors of 5379?

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 5379 by each of the numbers from 1 to 5379 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)

5379 / 1 = 5379 (the remainder is 0, so 1 is a divisor of 5379)
5379 / 2 = 2689.5 (the remainder is 1, so 2 is not a divisor of 5379)
5379 / 3 = 1793 (the remainder is 0, so 3 is a divisor of 5379)
...
5379 / 5378 = 1.0001859427296 (the remainder is 1, so 5378 is not a divisor of 5379)
5379 / 5379 = 1 (the remainder is 0, so 5379 is a divisor of 5379)

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 5379 (i.e. 73.341666193236). 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 $\frac{N}{d} = D$ )

5379 / 1 = 5379 (the remainder is 0, so 1 and 5379 are divisors of 5379)
5379 / 2 = 2689.5 (the remainder is 1, so 2 is not a divisor of 5379)
5379 / 3 = 1793 (the remainder is 0, so 3 and 1793 are divisors of 5379)
...
5379 / 72 = 74.708333333333 (the remainder is 51, so 72 is not a divisor of 5379)
5379 / 73 = 73.684931506849 (the remainder is 50, so 73 is not a divisor of 5379)