What are the divisors of 6055?

1, 5, 7, 35, 173, 865, 1211, 6055

There is a total of 8 positive divisors.
The sum of these divisors is 8352.
The arithmetic mean is 1044.

8 odd divisors

1, 5, 7, 35, 173, 865, 1211, 6055

How to compute the divisors of 6055?

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 6055 by each of the numbers from 1 to 6055 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)

6055 / 1 = 6055 (the remainder is 0, so 1 is a divisor of 6055)
6055 / 2 = 3027.5 (the remainder is 1, so 2 is not a divisor of 6055)
6055 / 3 = 2018.3333333333 (the remainder is 1, so 3 is not a divisor of 6055)
...
6055 / 6054 = 1.0001651800463 (the remainder is 1, so 6054 is not a divisor of 6055)
6055 / 6055 = 1 (the remainder is 0, so 6055 is a divisor of 6055)

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 6055 (i.e. 77.813880509842). 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 $\frac{N}{d} = D$ )

6055 / 1 = 6055 (the remainder is 0, so 1 and 6055 are divisors of 6055)
6055 / 2 = 3027.5 (the remainder is 1, so 2 is not a divisor of 6055)
6055 / 3 = 2018.3333333333 (the remainder is 1, so 3 is not a divisor of 6055)
...
6055 / 76 = 79.671052631579 (the remainder is 51, so 76 is not a divisor of 6055)
6055 / 77 = 78.636363636364 (the remainder is 49, so 77 is not a divisor of 6055)