What are the divisors of 1100?

1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550, 1100

There is a total of 18 positive divisors.
The sum of these divisors is 2604.
The arithmetic mean is 144.66666666667.

12 even divisors

2, 4, 10, 20, 22, 44, 50, 100, 110, 220, 550, 1100

6 odd divisors

1, 5, 11, 25, 55, 275

How to compute the divisors of 1100?

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 1100 by each of the numbers from 1 to 1100 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)

1100 / 1 = 1100 (the remainder is 0, so 1 is a divisor of 1100)
1100 / 2 = 550 (the remainder is 0, so 2 is a divisor of 1100)
1100 / 3 = 366.66666666667 (the remainder is 2, so 3 is not a divisor of 1100)
...
1100 / 1099 = 1.0009099181074 (the remainder is 1, so 1099 is not a divisor of 1100)
1100 / 1100 = 1 (the remainder is 0, so 1100 is a divisor of 1100)

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 1100 (i.e. 33.166247903554). 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 $\frac{N}{d} = D$ )

1100 / 1 = 1100 (the remainder is 0, so 1 and 1100 are divisors of 1100)
1100 / 2 = 550 (the remainder is 0, so 2 and 550 are divisors of 1100)
1100 / 3 = 366.66666666667 (the remainder is 2, so 3 is not a divisor of 1100)
...
1100 / 32 = 34.375 (the remainder is 12, so 32 is not a divisor of 1100)
1100 / 33 = 33.333333333333 (the remainder is 11, so 33 is not a divisor of 1100)