What are the divisors of 2206?

1, 2, 1103, 2206

There is a total of 4 positive divisors.
The sum of these divisors is 3312.
The arithmetic mean is 828.

2 even divisors

2, 2206

2 odd divisors

1, 1103

How to compute the divisors of 2206?

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 2206 by each of the numbers from 1 to 2206 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)

2206 / 1 = 2206 (the remainder is 0, so 1 is a divisor of 2206)
2206 / 2 = 1103 (the remainder is 0, so 2 is a divisor of 2206)
2206 / 3 = 735.33333333333 (the remainder is 1, so 3 is not a divisor of 2206)
...
2206 / 2205 = 1.0004535147392 (the remainder is 1, so 2205 is not a divisor of 2206)
2206 / 2206 = 1 (the remainder is 0, so 2206 is a divisor of 2206)

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 2206 (i.e. 46.96807426327). 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 $\frac{N}{d} = D$ )

2206 / 1 = 2206 (the remainder is 0, so 1 and 2206 are divisors of 2206)
2206 / 2 = 1103 (the remainder is 0, so 2 and 1103 are divisors of 2206)
2206 / 3 = 735.33333333333 (the remainder is 1, so 3 is not a divisor of 2206)
...
2206 / 45 = 49.022222222222 (the remainder is 1, so 45 is not a divisor of 2206)
2206 / 46 = 47.95652173913 (the remainder is 44, so 46 is not a divisor of 2206)