What are the divisors of 5463?

1, 3, 9, 607, 1821, 5463

There is a total of 6 positive divisors.
The sum of these divisors is 7904.
The arithmetic mean is 1317.3333333333.

6 odd divisors

1, 3, 9, 607, 1821, 5463

How to compute the divisors of 5463?

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 5463 by each of the numbers from 1 to 5463 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)

5463 / 1 = 5463 (the remainder is 0, so 1 is a divisor of 5463)
5463 / 2 = 2731.5 (the remainder is 1, so 2 is not a divisor of 5463)
5463 / 3 = 1821 (the remainder is 0, so 3 is a divisor of 5463)
...
5463 / 5462 = 1.0001830831197 (the remainder is 1, so 5462 is not a divisor of 5463)
5463 / 5463 = 1 (the remainder is 0, so 5463 is a divisor of 5463)

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 5463 (i.e. 73.91210996853). 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 $\frac{N}{d} = D$ )

5463 / 1 = 5463 (the remainder is 0, so 1 and 5463 are divisors of 5463)
5463 / 2 = 2731.5 (the remainder is 1, so 2 is not a divisor of 5463)
5463 / 3 = 1821 (the remainder is 0, so 3 and 1821 are divisors of 5463)
...
5463 / 72 = 75.875 (the remainder is 63, so 72 is not a divisor of 5463)
5463 / 73 = 74.835616438356 (the remainder is 61, so 73 is not a divisor of 5463)