What are the divisors of 5447?

1, 13, 419, 5447

There is a total of 4 positive divisors.
The sum of these divisors is 5880.
The arithmetic mean is 1470.

4 odd divisors

1, 13, 419, 5447

How to compute the divisors of 5447?

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 5447 by each of the numbers from 1 to 5447 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)

5447 / 1 = 5447 (the remainder is 0, so 1 is a divisor of 5447)
5447 / 2 = 2723.5 (the remainder is 1, so 2 is not a divisor of 5447)
5447 / 3 = 1815.6666666667 (the remainder is 2, so 3 is not a divisor of 5447)
...
5447 / 5446 = 1.0001836210062 (the remainder is 1, so 5446 is not a divisor of 5447)
5447 / 5447 = 1 (the remainder is 0, so 5447 is a divisor of 5447)

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 5447 (i.e. 73.80379394042). 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 $\frac{N}{d} = D$ )

5447 / 1 = 5447 (the remainder is 0, so 1 and 5447 are divisors of 5447)
5447 / 2 = 2723.5 (the remainder is 1, so 2 is not a divisor of 5447)
5447 / 3 = 1815.6666666667 (the remainder is 2, so 3 is not a divisor of 5447)
...
5447 / 72 = 75.652777777778 (the remainder is 47, so 72 is not a divisor of 5447)
5447 / 73 = 74.616438356164 (the remainder is 45, so 73 is not a divisor of 5447)