What are the divisors of 5361?

1, 3, 1787, 5361

There is a total of 4 positive divisors.
The sum of these divisors is 7152.
The arithmetic mean is 1788.

4 odd divisors

1, 3, 1787, 5361

How to compute the divisors of 5361?

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 5361 by each of the numbers from 1 to 5361 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)

5361 / 1 = 5361 (the remainder is 0, so 1 is a divisor of 5361)
5361 / 2 = 2680.5 (the remainder is 1, so 2 is not a divisor of 5361)
5361 / 3 = 1787 (the remainder is 0, so 3 is a divisor of 5361)
...
5361 / 5360 = 1.0001865671642 (the remainder is 1, so 5360 is not a divisor of 5361)
5361 / 5361 = 1 (the remainder is 0, so 5361 is a divisor of 5361)

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 5361 (i.e. 73.218850031942). 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 $\frac{N}{d} = D$ )

5361 / 1 = 5361 (the remainder is 0, so 1 and 5361 are divisors of 5361)
5361 / 2 = 2680.5 (the remainder is 1, so 2 is not a divisor of 5361)
5361 / 3 = 1787 (the remainder is 0, so 3 and 1787 are divisors of 5361)
...
5361 / 72 = 74.458333333333 (the remainder is 33, so 72 is not a divisor of 5361)
5361 / 73 = 73.438356164384 (the remainder is 32, so 73 is not a divisor of 5361)