What are the divisors of 4400?

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 25, 40, 44, 50, 55, 80, 88, 100, 110, 176, 200, 220, 275, 400, 440, 550, 880, 1100, 2200, 4400

There is a total of 30 positive divisors.
The sum of these divisors is 11532.
The arithmetic mean is 384.4.

24 even divisors

2, 4, 8, 10, 16, 20, 22, 40, 44, 50, 80, 88, 100, 110, 176, 200, 220, 400, 440, 550, 880, 1100, 2200, 4400

6 odd divisors

1, 5, 11, 25, 55, 275

How to compute the divisors of 4400?

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 4400 by each of the numbers from 1 to 4400 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)

4400 / 1 = 4400 (the remainder is 0, so 1 is a divisor of 4400)
4400 / 2 = 2200 (the remainder is 0, so 2 is a divisor of 4400)
4400 / 3 = 1466.6666666667 (the remainder is 2, so 3 is not a divisor of 4400)
...
4400 / 4399 = 1.0002273243919 (the remainder is 1, so 4399 is not a divisor of 4400)
4400 / 4400 = 1 (the remainder is 0, so 4400 is a divisor of 4400)

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 4400 (i.e. 66.332495807108). 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 $\frac{N}{d} = D$ )

4400 / 1 = 4400 (the remainder is 0, so 1 and 4400 are divisors of 4400)
4400 / 2 = 2200 (the remainder is 0, so 2 and 2200 are divisors of 4400)
4400 / 3 = 1466.6666666667 (the remainder is 2, so 3 is not a divisor of 4400)
...
4400 / 65 = 67.692307692308 (the remainder is 45, so 65 is not a divisor of 4400)
4400 / 66 = 66.666666666667 (the remainder is 44, so 66 is not a divisor of 4400)