What are the divisors of 5649?

1, 3, 7, 21, 269, 807, 1883, 5649

There is a total of 8 positive divisors.
The sum of these divisors is 8640.
The arithmetic mean is 1080.

8 odd divisors

1, 3, 7, 21, 269, 807, 1883, 5649

How to compute the divisors of 5649?

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 5649 by each of the numbers from 1 to 5649 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)

5649 / 1 = 5649 (the remainder is 0, so 1 is a divisor of 5649)
5649 / 2 = 2824.5 (the remainder is 1, so 2 is not a divisor of 5649)
5649 / 3 = 1883 (the remainder is 0, so 3 is a divisor of 5649)
...
5649 / 5648 = 1.0001770538244 (the remainder is 1, so 5648 is not a divisor of 5649)
5649 / 5649 = 1 (the remainder is 0, so 5649 is a divisor of 5649)

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 5649 (i.e. 75.159829696454). 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 $\frac{N}{d} = D$ )

5649 / 1 = 5649 (the remainder is 0, so 1 and 5649 are divisors of 5649)
5649 / 2 = 2824.5 (the remainder is 1, so 2 is not a divisor of 5649)
5649 / 3 = 1883 (the remainder is 0, so 3 and 1883 are divisors of 5649)
...
5649 / 74 = 76.337837837838 (the remainder is 25, so 74 is not a divisor of 5649)
5649 / 75 = 75.32 (the remainder is 24, so 75 is not a divisor of 5649)