What are the divisors of 5107?

1, 5107

There is a total of 2 positive divisors.
The sum of these divisors is 5108.
The arithmetic mean is 2554.

2 odd divisors

1, 5107

How to compute the divisors of 5107?

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 5107 by each of the numbers from 1 to 5107 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)

5107 / 1 = 5107 (the remainder is 0, so 1 is a divisor of 5107)
5107 / 2 = 2553.5 (the remainder is 1, so 2 is not a divisor of 5107)
5107 / 3 = 1702.3333333333 (the remainder is 1, so 3 is not a divisor of 5107)
...
5107 / 5106 = 1.0001958480219 (the remainder is 1, so 5106 is not a divisor of 5107)
5107 / 5107 = 1 (the remainder is 0, so 5107 is a divisor of 5107)

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 5107 (i.e. 71.463277282811). 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 $\frac{N}{d} = D$ )

5107 / 1 = 5107 (the remainder is 0, so 1 and 5107 are divisors of 5107)
5107 / 2 = 2553.5 (the remainder is 1, so 2 is not a divisor of 5107)
5107 / 3 = 1702.3333333333 (the remainder is 1, so 3 is not a divisor of 5107)
...
5107 / 70 = 72.957142857143 (the remainder is 67, so 70 is not a divisor of 5107)
5107 / 71 = 71.929577464789 (the remainder is 66, so 71 is not a divisor of 5107)