What are the divisors of 5055?

1, 3, 5, 15, 337, 1011, 1685, 5055

There is a total of 8 positive divisors.
The sum of these divisors is 8112.
The arithmetic mean is 1014.

8 odd divisors

1, 3, 5, 15, 337, 1011, 1685, 5055

How to compute the divisors of 5055?

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 5055 by each of the numbers from 1 to 5055 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)

5055 / 1 = 5055 (the remainder is 0, so 1 is a divisor of 5055)
5055 / 2 = 2527.5 (the remainder is 1, so 2 is not a divisor of 5055)
5055 / 3 = 1685 (the remainder is 0, so 3 is a divisor of 5055)
...
5055 / 5054 = 1.0001978630787 (the remainder is 1, so 5054 is not a divisor of 5055)
5055 / 5055 = 1 (the remainder is 0, so 5055 is a divisor of 5055)

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 5055 (i.e. 71.098523191414). 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 $\frac{N}{d} = D$ )

5055 / 1 = 5055 (the remainder is 0, so 1 and 5055 are divisors of 5055)
5055 / 2 = 2527.5 (the remainder is 1, so 2 is not a divisor of 5055)
5055 / 3 = 1685 (the remainder is 0, so 3 and 1685 are divisors of 5055)
...
5055 / 70 = 72.214285714286 (the remainder is 15, so 70 is not a divisor of 5055)
5055 / 71 = 71.197183098592 (the remainder is 14, so 71 is not a divisor of 5055)