What are the divisors of 5127?

1, 3, 1709, 5127

There is a total of 4 positive divisors.
The sum of these divisors is 6840.
The arithmetic mean is 1710.

4 odd divisors

1, 3, 1709, 5127

How to compute the divisors of 5127?

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 5127 by each of the numbers from 1 to 5127 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)

5127 / 1 = 5127 (the remainder is 0, so 1 is a divisor of 5127)
5127 / 2 = 2563.5 (the remainder is 1, so 2 is not a divisor of 5127)
5127 / 3 = 1709 (the remainder is 0, so 3 is a divisor of 5127)
...
5127 / 5126 = 1.0001950838861 (the remainder is 1, so 5126 is not a divisor of 5127)
5127 / 5127 = 1 (the remainder is 0, so 5127 is a divisor of 5127)

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 5127 (i.e. 71.603072559772). 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 $\frac{N}{d} = D$ )

5127 / 1 = 5127 (the remainder is 0, so 1 and 5127 are divisors of 5127)
5127 / 2 = 2563.5 (the remainder is 1, so 2 is not a divisor of 5127)
5127 / 3 = 1709 (the remainder is 0, so 3 and 1709 are divisors of 5127)
...
5127 / 70 = 73.242857142857 (the remainder is 17, so 70 is not a divisor of 5127)
5127 / 71 = 72.211267605634 (the remainder is 15, so 71 is not a divisor of 5127)