What are the divisors of 2855?

1, 5, 571, 2855

There is a total of 4 positive divisors.
The sum of these divisors is 3432.
The arithmetic mean is 858.

4 odd divisors

1, 5, 571, 2855

How to compute the divisors of 2855?

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 2855 by each of the numbers from 1 to 2855 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)

2855 / 1 = 2855 (the remainder is 0, so 1 is a divisor of 2855)
2855 / 2 = 1427.5 (the remainder is 1, so 2 is not a divisor of 2855)
2855 / 3 = 951.66666666667 (the remainder is 2, so 3 is not a divisor of 2855)
...
2855 / 2854 = 1.000350385424 (the remainder is 1, so 2854 is not a divisor of 2855)
2855 / 2855 = 1 (the remainder is 0, so 2855 is a divisor of 2855)

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 2855 (i.e. 53.43220002957). 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 $\frac{N}{d} = D$ )

2855 / 1 = 2855 (the remainder is 0, so 1 and 2855 are divisors of 2855)
2855 / 2 = 1427.5 (the remainder is 1, so 2 is not a divisor of 2855)
2855 / 3 = 951.66666666667 (the remainder is 2, so 3 is not a divisor of 2855)
...
2855 / 52 = 54.903846153846 (the remainder is 47, so 52 is not a divisor of 2855)
2855 / 53 = 53.867924528302 (the remainder is 46, so 53 is not a divisor of 2855)