What are the divisors of 4166?

1, 2, 2083, 4166

There is a total of 4 positive divisors.
The sum of these divisors is 6252.
The arithmetic mean is 1563.

2 even divisors

2, 4166

2 odd divisors

1, 2083

How to compute the divisors of 4166?

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 4166 by each of the numbers from 1 to 4166 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)

4166 / 1 = 4166 (the remainder is 0, so 1 is a divisor of 4166)
4166 / 2 = 2083 (the remainder is 0, so 2 is a divisor of 4166)
4166 / 3 = 1388.6666666667 (the remainder is 2, so 3 is not a divisor of 4166)
...
4166 / 4165 = 1.0002400960384 (the remainder is 1, so 4165 is not a divisor of 4166)
4166 / 4166 = 1 (the remainder is 0, so 4166 is a divisor of 4166)

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 4166 (i.e. 64.54455825242). 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 $\frac{N}{d} = D$ )

4166 / 1 = 4166 (the remainder is 0, so 1 and 4166 are divisors of 4166)
4166 / 2 = 2083 (the remainder is 0, so 2 and 2083 are divisors of 4166)
4166 / 3 = 1388.6666666667 (the remainder is 2, so 3 is not a divisor of 4166)
...
4166 / 63 = 66.126984126984 (the remainder is 8, so 63 is not a divisor of 4166)
4166 / 64 = 65.09375 (the remainder is 6, so 64 is not a divisor of 4166)