What are the divisors of 5427?

1, 3, 9, 27, 67, 81, 201, 603, 1809, 5427

There is a total of 10 positive divisors.
The sum of these divisors is 8228.
The arithmetic mean is 822.8.

10 odd divisors

1, 3, 9, 27, 67, 81, 201, 603, 1809, 5427

How to compute the divisors of 5427?

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 5427 by each of the numbers from 1 to 5427 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)

5427 / 1 = 5427 (the remainder is 0, so 1 is a divisor of 5427)
5427 / 2 = 2713.5 (the remainder is 1, so 2 is not a divisor of 5427)
5427 / 3 = 1809 (the remainder is 0, so 3 is a divisor of 5427)
...
5427 / 5426 = 1.0001842978253 (the remainder is 1, so 5426 is not a divisor of 5427)
5427 / 5427 = 1 (the remainder is 0, so 5427 is a divisor of 5427)

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 5427 (i.e. 73.668174946852). 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 $\frac{N}{d} = D$ )

5427 / 1 = 5427 (the remainder is 0, so 1 and 5427 are divisors of 5427)
5427 / 2 = 2713.5 (the remainder is 1, so 2 is not a divisor of 5427)
5427 / 3 = 1809 (the remainder is 0, so 3 and 1809 are divisors of 5427)
...
5427 / 72 = 75.375 (the remainder is 27, so 72 is not a divisor of 5427)
5427 / 73 = 74.342465753425 (the remainder is 25, so 73 is not a divisor of 5427)