What are the divisors of 5647?

1, 5647

There is a total of 2 positive divisors.
The sum of these divisors is 5648.
The arithmetic mean is 2824.

2 odd divisors

1, 5647

How to compute the divisors of 5647?

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 5647 by each of the numbers from 1 to 5647 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)

5647 / 1 = 5647 (the remainder is 0, so 1 is a divisor of 5647)
5647 / 2 = 2823.5 (the remainder is 1, so 2 is not a divisor of 5647)
5647 / 3 = 1882.3333333333 (the remainder is 1, so 3 is not a divisor of 5647)
...
5647 / 5646 = 1.0001771165427 (the remainder is 1, so 5646 is not a divisor of 5647)
5647 / 5647 = 1 (the remainder is 0, so 5647 is a divisor of 5647)

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 5647 (i.e. 75.146523539017). 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 $\frac{N}{d} = D$ )

5647 / 1 = 5647 (the remainder is 0, so 1 and 5647 are divisors of 5647)
5647 / 2 = 2823.5 (the remainder is 1, so 2 is not a divisor of 5647)
5647 / 3 = 1882.3333333333 (the remainder is 1, so 3 is not a divisor of 5647)
...
5647 / 74 = 76.310810810811 (the remainder is 23, so 74 is not a divisor of 5647)
5647 / 75 = 75.293333333333 (the remainder is 22, so 75 is not a divisor of 5647)