What are the divisors of 2200?

1, 2, 4, 5, 8, 10, 11, 20, 22, 25, 40, 44, 50, 55, 88, 100, 110, 200, 220, 275, 440, 550, 1100, 2200

There is a total of 24 positive divisors.
The sum of these divisors is 5580.
The arithmetic mean is 232.5.

18 even divisors

2, 4, 8, 10, 20, 22, 40, 44, 50, 88, 100, 110, 200, 220, 440, 550, 1100, 2200

6 odd divisors

1, 5, 11, 25, 55, 275

How to compute the divisors of 2200?

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 2200 by each of the numbers from 1 to 2200 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)

2200 / 1 = 2200 (the remainder is 0, so 1 is a divisor of 2200)
2200 / 2 = 1100 (the remainder is 0, so 2 is a divisor of 2200)
2200 / 3 = 733.33333333333 (the remainder is 1, so 3 is not a divisor of 2200)
...
2200 / 2199 = 1.0004547521601 (the remainder is 1, so 2199 is not a divisor of 2200)
2200 / 2200 = 1 (the remainder is 0, so 2200 is a divisor of 2200)

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 2200 (i.e. 46.904157598234). 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 $\frac{N}{d} = D$ )

2200 / 1 = 2200 (the remainder is 0, so 1 and 2200 are divisors of 2200)
2200 / 2 = 1100 (the remainder is 0, so 2 and 1100 are divisors of 2200)
2200 / 3 = 733.33333333333 (the remainder is 1, so 3 is not a divisor of 2200)
...
2200 / 45 = 48.888888888889 (the remainder is 40, so 45 is not a divisor of 2200)
2200 / 46 = 47.826086956522 (the remainder is 38, so 46 is not a divisor of 2200)