What are the divisors of 5126?

1, 2, 11, 22, 233, 466, 2563, 5126

There is a total of 8 positive divisors.
The sum of these divisors is 8424.
The arithmetic mean is 1053.

4 even divisors

2, 22, 466, 5126

4 odd divisors

1, 11, 233, 2563

How to compute the divisors of 5126?

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 5126 by each of the numbers from 1 to 5126 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)

5126 / 1 = 5126 (the remainder is 0, so 1 is a divisor of 5126)
5126 / 2 = 2563 (the remainder is 0, so 2 is a divisor of 5126)
5126 / 3 = 1708.6666666667 (the remainder is 2, so 3 is not a divisor of 5126)
...
5126 / 5125 = 1.0001951219512 (the remainder is 1, so 5125 is not a divisor of 5126)
5126 / 5126 = 1 (the remainder is 0, so 5126 is a divisor of 5126)

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 5126 (i.e. 71.596089278675). 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 $\frac{N}{d} = D$ )

5126 / 1 = 5126 (the remainder is 0, so 1 and 5126 are divisors of 5126)
5126 / 2 = 2563 (the remainder is 0, so 2 and 2563 are divisors of 5126)
5126 / 3 = 1708.6666666667 (the remainder is 2, so 3 is not a divisor of 5126)
...
5126 / 70 = 73.228571428571 (the remainder is 16, so 70 is not a divisor of 5126)
5126 / 71 = 72.197183098592 (the remainder is 14, so 71 is not a divisor of 5126)