What are the divisors of 4255?

1, 5, 23, 37, 115, 185, 851, 4255

There is a total of 8 positive divisors.
The sum of these divisors is 5472.
The arithmetic mean is 684.

8 odd divisors

1, 5, 23, 37, 115, 185, 851, 4255

How to compute the divisors of 4255?

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 4255 by each of the numbers from 1 to 4255 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)

4255 / 1 = 4255 (the remainder is 0, so 1 is a divisor of 4255)
4255 / 2 = 2127.5 (the remainder is 1, so 2 is not a divisor of 4255)
4255 / 3 = 1418.3333333333 (the remainder is 1, so 3 is not a divisor of 4255)
...
4255 / 4254 = 1.0002350728726 (the remainder is 1, so 4254 is not a divisor of 4255)
4255 / 4255 = 1 (the remainder is 0, so 4255 is a divisor of 4255)

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 4255 (i.e. 65.230361029202). 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 $\frac{N}{d} = D$ )

4255 / 1 = 4255 (the remainder is 0, so 1 and 4255 are divisors of 4255)
4255 / 2 = 2127.5 (the remainder is 1, so 2 is not a divisor of 4255)
4255 / 3 = 1418.3333333333 (the remainder is 1, so 3 is not a divisor of 4255)
...
4255 / 64 = 66.484375 (the remainder is 31, so 64 is not a divisor of 4255)
4255 / 65 = 65.461538461538 (the remainder is 30, so 65 is not a divisor of 4255)