What are the divisors of 4126?

1, 2, 2063, 4126

There is a total of 4 positive divisors.
The sum of these divisors is 6192.
The arithmetic mean is 1548.

2 even divisors

2, 4126

2 odd divisors

1, 2063

How to compute the divisors of 4126?

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 4126 by each of the numbers from 1 to 4126 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)

4126 / 1 = 4126 (the remainder is 0, so 1 is a divisor of 4126)
4126 / 2 = 2063 (the remainder is 0, so 2 is a divisor of 4126)
4126 / 3 = 1375.3333333333 (the remainder is 1, so 3 is not a divisor of 4126)
...
4126 / 4125 = 1.0002424242424 (the remainder is 1, so 4125 is not a divisor of 4126)
4126 / 4126 = 1 (the remainder is 0, so 4126 is a divisor of 4126)

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 4126 (i.e. 64.233947411007). 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 $\frac{N}{d} = D$ )

4126 / 1 = 4126 (the remainder is 0, so 1 and 4126 are divisors of 4126)
4126 / 2 = 2063 (the remainder is 0, so 2 and 2063 are divisors of 4126)
4126 / 3 = 1375.3333333333 (the remainder is 1, so 3 is not a divisor of 4126)
...
4126 / 63 = 65.492063492063 (the remainder is 31, so 63 is not a divisor of 4126)
4126 / 64 = 64.46875 (the remainder is 30, so 64 is not a divisor of 4126)