What are the divisors of 206?

1, 2, 103, 206

There is a total of 4 positive divisors.
The sum of these divisors is 312.
The arithmetic mean is 78.

2 even divisors

2, 206

2 odd divisors

1, 103

How to compute the divisors of 206?

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 206 by each of the numbers from 1 to 206 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)

206 / 1 = 206 (the remainder is 0, so 1 is a divisor of 206)
206 / 2 = 103 (the remainder is 0, so 2 is a divisor of 206)
206 / 3 = 68.666666666667 (the remainder is 2, so 3 is not a divisor of 206)
...
206 / 205 = 1.0048780487805 (the remainder is 1, so 205 is not a divisor of 206)
206 / 206 = 1 (the remainder is 0, so 206 is a divisor of 206)

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 206 (i.e. 14.352700094407). 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 $\frac{N}{d} = D$ )

206 / 1 = 206 (the remainder is 0, so 1 and 206 are divisors of 206)
206 / 2 = 103 (the remainder is 0, so 2 and 103 are divisors of 206)
206 / 3 = 68.666666666667 (the remainder is 2, so 3 is not a divisor of 206)
...
206 / 13 = 15.846153846154 (the remainder is 11, so 13 is not a divisor of 206)
206 / 14 = 14.714285714286 (the remainder is 10, so 14 is not a divisor of 206)