What are the divisors of 4106?

1, 2, 2053, 4106

There is a total of 4 positive divisors.
The sum of these divisors is 6162.
The arithmetic mean is 1540.5.

2 even divisors

2, 4106

2 odd divisors

1, 2053

How to compute the divisors of 4106?

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 4106 by each of the numbers from 1 to 4106 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)

4106 / 1 = 4106 (the remainder is 0, so 1 is a divisor of 4106)
4106 / 2 = 2053 (the remainder is 0, so 2 is a divisor of 4106)
4106 / 3 = 1368.6666666667 (the remainder is 2, so 3 is not a divisor of 4106)
...
4106 / 4105 = 1.0002436053593 (the remainder is 1, so 4105 is not a divisor of 4106)
4106 / 4106 = 1 (the remainder is 0, so 4106 is a divisor of 4106)

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 4106 (i.e. 64.078077374403). 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 $\frac{N}{d} = D$ )

4106 / 1 = 4106 (the remainder is 0, so 1 and 4106 are divisors of 4106)
4106 / 2 = 2053 (the remainder is 0, so 2 and 2053 are divisors of 4106)
4106 / 3 = 1368.6666666667 (the remainder is 2, so 3 is not a divisor of 4106)
...
4106 / 63 = 65.174603174603 (the remainder is 11, so 63 is not a divisor of 4106)
4106 / 64 = 64.15625 (the remainder is 10, so 64 is not a divisor of 4106)