What are the divisors of 5255?

1, 5, 1051, 5255

There is a total of 4 positive divisors.
The sum of these divisors is 6312.
The arithmetic mean is 1578.

4 odd divisors

1, 5, 1051, 5255

How to compute the divisors of 5255?

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 5255 by each of the numbers from 1 to 5255 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)

5255 / 1 = 5255 (the remainder is 0, so 1 is a divisor of 5255)
5255 / 2 = 2627.5 (the remainder is 1, so 2 is not a divisor of 5255)
5255 / 3 = 1751.6666666667 (the remainder is 2, so 3 is not a divisor of 5255)
...
5255 / 5254 = 1.0001903311762 (the remainder is 1, so 5254 is not a divisor of 5255)
5255 / 5255 = 1 (the remainder is 0, so 5255 is a divisor of 5255)

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 5255 (i.e. 72.491378797758). 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 $\frac{N}{d} = D$ )

5255 / 1 = 5255 (the remainder is 0, so 1 and 5255 are divisors of 5255)
5255 / 2 = 2627.5 (the remainder is 1, so 2 is not a divisor of 5255)
5255 / 3 = 1751.6666666667 (the remainder is 2, so 3 is not a divisor of 5255)
...
5255 / 71 = 74.014084507042 (the remainder is 1, so 71 is not a divisor of 5255)
5255 / 72 = 72.986111111111 (the remainder is 71, so 72 is not a divisor of 5255)