What are the divisors of 5909?

1, 19, 311, 5909

There is a total of 4 positive divisors.
The sum of these divisors is 6240.
The arithmetic mean is 1560.

4 odd divisors

1, 19, 311, 5909

How to compute the divisors of 5909?

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 5909 by each of the numbers from 1 to 5909 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)

5909 / 1 = 5909 (the remainder is 0, so 1 is a divisor of 5909)
5909 / 2 = 2954.5 (the remainder is 1, so 2 is not a divisor of 5909)
5909 / 3 = 1969.6666666667 (the remainder is 2, so 3 is not a divisor of 5909)
...
5909 / 5908 = 1.0001692620176 (the remainder is 1, so 5908 is not a divisor of 5909)
5909 / 5909 = 1 (the remainder is 0, so 5909 is a divisor of 5909)

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 5909 (i.e. 76.87002016391). 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 $\frac{N}{d} = D$ )

5909 / 1 = 5909 (the remainder is 0, so 1 and 5909 are divisors of 5909)
5909 / 2 = 2954.5 (the remainder is 1, so 2 is not a divisor of 5909)
5909 / 3 = 1969.6666666667 (the remainder is 2, so 3 is not a divisor of 5909)
...
5909 / 75 = 78.786666666667 (the remainder is 59, so 75 is not a divisor of 5909)
5909 / 76 = 77.75 (the remainder is 57, so 76 is not a divisor of 5909)