What are the divisors of 6109?

1, 41, 149, 6109

There is a total of 4 positive divisors.
The sum of these divisors is 6300.
The arithmetic mean is 1575.

4 odd divisors

1, 41, 149, 6109

How to compute the divisors of 6109?

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 6109 by each of the numbers from 1 to 6109 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)

6109 / 1 = 6109 (the remainder is 0, so 1 is a divisor of 6109)
6109 / 2 = 3054.5 (the remainder is 1, so 2 is not a divisor of 6109)
6109 / 3 = 2036.3333333333 (the remainder is 1, so 3 is not a divisor of 6109)
...
6109 / 6108 = 1.0001637197119 (the remainder is 1, so 6108 is not a divisor of 6109)
6109 / 6109 = 1 (the remainder is 0, so 6109 is a divisor of 6109)

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 6109 (i.e. 78.160092118677). 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 $\frac{N}{d} = D$ )

6109 / 1 = 6109 (the remainder is 0, so 1 and 6109 are divisors of 6109)
6109 / 2 = 3054.5 (the remainder is 1, so 2 is not a divisor of 6109)
6109 / 3 = 2036.3333333333 (the remainder is 1, so 3 is not a divisor of 6109)
...
6109 / 77 = 79.337662337662 (the remainder is 26, so 77 is not a divisor of 6109)
6109 / 78 = 78.320512820513 (the remainder is 25, so 78 is not a divisor of 6109)