What are the divisors of 5609?

1, 71, 79, 5609

There is a total of 4 positive divisors.
The sum of these divisors is 5760.
The arithmetic mean is 1440.

4 odd divisors

1, 71, 79, 5609

How to compute the divisors of 5609?

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 5609 by each of the numbers from 1 to 5609 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)

5609 / 1 = 5609 (the remainder is 0, so 1 is a divisor of 5609)
5609 / 2 = 2804.5 (the remainder is 1, so 2 is not a divisor of 5609)
5609 / 3 = 1869.6666666667 (the remainder is 2, so 3 is not a divisor of 5609)
...
5609 / 5608 = 1.0001783166904 (the remainder is 1, so 5608 is not a divisor of 5609)
5609 / 5609 = 1 (the remainder is 0, so 5609 is a divisor of 5609)

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 5609 (i.e. 74.893257373411). 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 $\frac{N}{d} = D$ )

5609 / 1 = 5609 (the remainder is 0, so 1 and 5609 are divisors of 5609)
5609 / 2 = 2804.5 (the remainder is 1, so 2 is not a divisor of 5609)
5609 / 3 = 1869.6666666667 (the remainder is 2, so 3 is not a divisor of 5609)
...
5609 / 73 = 76.835616438356 (the remainder is 61, so 73 is not a divisor of 5609)
5609 / 74 = 75.797297297297 (the remainder is 59, so 74 is not a divisor of 5609)