What are the divisors of 6155?

1, 5, 1231, 6155

There is a total of 4 positive divisors.
The sum of these divisors is 7392.
The arithmetic mean is 1848.

4 odd divisors

1, 5, 1231, 6155

How to compute the divisors of 6155?

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 6155 by each of the numbers from 1 to 6155 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)

6155 / 1 = 6155 (the remainder is 0, so 1 is a divisor of 6155)
6155 / 2 = 3077.5 (the remainder is 1, so 2 is not a divisor of 6155)
6155 / 3 = 2051.6666666667 (the remainder is 2, so 3 is not a divisor of 6155)
...
6155 / 6154 = 1.0001624959376 (the remainder is 1, so 6154 is not a divisor of 6155)
6155 / 6155 = 1 (the remainder is 0, so 6155 is a divisor of 6155)

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 6155 (i.e. 78.453808065638). 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 $\frac{N}{d} = D$ )

6155 / 1 = 6155 (the remainder is 0, so 1 and 6155 are divisors of 6155)
6155 / 2 = 3077.5 (the remainder is 1, so 2 is not a divisor of 6155)
6155 / 3 = 2051.6666666667 (the remainder is 2, so 3 is not a divisor of 6155)
...
6155 / 77 = 79.935064935065 (the remainder is 72, so 77 is not a divisor of 6155)
6155 / 78 = 78.910256410256 (the remainder is 71, so 78 is not a divisor of 6155)