What are the divisors of 2209?

1, 47, 2209

There is a total of 3 positive divisors.
The sum of these divisors is 2257.
The arithmetic mean is 752.33333333333.

3 odd divisors

1, 47, 2209

How to compute the divisors of 2209?

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 2209 by each of the numbers from 1 to 2209 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)

2209 / 1 = 2209 (the remainder is 0, so 1 is a divisor of 2209)
2209 / 2 = 1104.5 (the remainder is 1, so 2 is not a divisor of 2209)
2209 / 3 = 736.33333333333 (the remainder is 1, so 3 is not a divisor of 2209)
...
2209 / 2208 = 1.0004528985507 (the remainder is 1, so 2208 is not a divisor of 2209)
2209 / 2209 = 1 (the remainder is 0, so 2209 is a divisor of 2209)

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 2209 (i.e. 47). 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 $\frac{N}{d} = D$ )

2209 / 1 = 2209 (the remainder is 0, so 1 and 2209 are divisors of 2209)
2209 / 2 = 1104.5 (the remainder is 1, so 2 is not a divisor of 2209)
2209 / 3 = 736.33333333333 (the remainder is 1, so 3 is not a divisor of 2209)
...
2209 / 46 = 48.021739130435 (the remainder is 1, so 46 is not a divisor of 2209)
2209 / 47 = 47 (the remainder is 0, so 47 and 47 are divisors of 2209)