What are the divisors of 4206?

1, 2, 3, 6, 701, 1402, 2103, 4206

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

4 even divisors

2, 6, 1402, 4206

4 odd divisors

1, 3, 701, 2103

How to compute the divisors of 4206?

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 4206 by each of the numbers from 1 to 4206 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)

4206 / 1 = 4206 (the remainder is 0, so 1 is a divisor of 4206)
4206 / 2 = 2103 (the remainder is 0, so 2 is a divisor of 4206)
4206 / 3 = 1402 (the remainder is 0, so 3 is a divisor of 4206)
...
4206 / 4205 = 1.0002378121284 (the remainder is 1, so 4205 is not a divisor of 4206)
4206 / 4206 = 1 (the remainder is 0, so 4206 is a divisor of 4206)

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 4206 (i.e. 64.853681468364). 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 $\frac{N}{d} = D$ )

4206 / 1 = 4206 (the remainder is 0, so 1 and 4206 are divisors of 4206)
4206 / 2 = 2103 (the remainder is 0, so 2 and 2103 are divisors of 4206)
4206 / 3 = 1402 (the remainder is 0, so 3 and 1402 are divisors of 4206)
...
4206 / 63 = 66.761904761905 (the remainder is 48, so 63 is not a divisor of 4206)
4206 / 64 = 65.71875 (the remainder is 46, so 64 is not a divisor of 4206)