What are the divisors of 2555?

1, 5, 7, 35, 73, 365, 511, 2555

There is a total of 8 positive divisors.
The sum of these divisors is 3552.
The arithmetic mean is 444.

8 odd divisors

1, 5, 7, 35, 73, 365, 511, 2555

How to compute the divisors of 2555?

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 2555 by each of the numbers from 1 to 2555 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)

2555 / 1 = 2555 (the remainder is 0, so 1 is a divisor of 2555)
2555 / 2 = 1277.5 (the remainder is 1, so 2 is not a divisor of 2555)
2555 / 3 = 851.66666666667 (the remainder is 2, so 3 is not a divisor of 2555)
...
2555 / 2554 = 1.0003915426782 (the remainder is 1, so 2554 is not a divisor of 2555)
2555 / 2555 = 1 (the remainder is 0, so 2555 is a divisor of 2555)

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 2555 (i.e. 50.5470078244). 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 $\frac{N}{d} = D$ )

2555 / 1 = 2555 (the remainder is 0, so 1 and 2555 are divisors of 2555)
2555 / 2 = 1277.5 (the remainder is 1, so 2 is not a divisor of 2555)
2555 / 3 = 851.66666666667 (the remainder is 2, so 3 is not a divisor of 2555)
...
2555 / 49 = 52.142857142857 (the remainder is 7, so 49 is not a divisor of 2555)
2555 / 50 = 51.1 (the remainder is 5, so 50 is not a divisor of 2555)