What are the divisors of 6110?

1, 2, 5, 10, 13, 26, 47, 65, 94, 130, 235, 470, 611, 1222, 3055, 6110

There is a total of 16 positive divisors.
The sum of these divisors is 12096.
The arithmetic mean is 756.

8 even divisors

2, 10, 26, 94, 130, 470, 1222, 6110

8 odd divisors

1, 5, 13, 47, 65, 235, 611, 3055

How to compute the divisors of 6110?

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 6110 by each of the numbers from 1 to 6110 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)

6110 / 1 = 6110 (the remainder is 0, so 1 is a divisor of 6110)
6110 / 2 = 3055 (the remainder is 0, so 2 is a divisor of 6110)
6110 / 3 = 2036.6666666667 (the remainder is 2, so 3 is not a divisor of 6110)
...
6110 / 6109 = 1.0001636929121 (the remainder is 1, so 6109 is not a divisor of 6110)
6110 / 6110 = 1 (the remainder is 0, so 6110 is a divisor of 6110)

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 6110 (i.e. 78.166488983451). 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 $\frac{N}{d} = D$ )

6110 / 1 = 6110 (the remainder is 0, so 1 and 6110 are divisors of 6110)
6110 / 2 = 3055 (the remainder is 0, so 2 and 3055 are divisors of 6110)
6110 / 3 = 2036.6666666667 (the remainder is 2, so 3 is not a divisor of 6110)
...
6110 / 77 = 79.350649350649 (the remainder is 27, so 77 is not a divisor of 6110)
6110 / 78 = 78.333333333333 (the remainder is 26, so 78 is not a divisor of 6110)