What are the divisors of 1101?

1, 3, 367, 1101

There is a total of 4 positive divisors.
The sum of these divisors is 1472.
The arithmetic mean is 368.

4 odd divisors

1, 3, 367, 1101

How to compute the divisors of 1101?

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 1101 by each of the numbers from 1 to 1101 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)

1101 / 1 = 1101 (the remainder is 0, so 1 is a divisor of 1101)
1101 / 2 = 550.5 (the remainder is 1, so 2 is not a divisor of 1101)
1101 / 3 = 367 (the remainder is 0, so 3 is a divisor of 1101)
...
1101 / 1100 = 1.0009090909091 (the remainder is 1, so 1100 is not a divisor of 1101)
1101 / 1101 = 1 (the remainder is 0, so 1101 is a divisor of 1101)

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 1101 (i.e. 33.181320046074). 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 $\frac{N}{d} = D$ )

1101 / 1 = 1101 (the remainder is 0, so 1 and 1101 are divisors of 1101)
1101 / 2 = 550.5 (the remainder is 1, so 2 is not a divisor of 1101)
1101 / 3 = 367 (the remainder is 0, so 3 and 367 are divisors of 1101)
...
1101 / 32 = 34.40625 (the remainder is 13, so 32 is not a divisor of 1101)
1101 / 33 = 33.363636363636 (the remainder is 12, so 33 is not a divisor of 1101)