What are the divisors of 909?

1, 3, 9, 101, 303, 909

There is a total of 6 positive divisors.
The sum of these divisors is 1326.
The arithmetic mean is 221.

6 odd divisors

1, 3, 9, 101, 303, 909

How to compute the divisors of 909?

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 909 by each of the numbers from 1 to 909 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)

909 / 1 = 909 (the remainder is 0, so 1 is a divisor of 909)
909 / 2 = 454.5 (the remainder is 1, so 2 is not a divisor of 909)
909 / 3 = 303 (the remainder is 0, so 3 is a divisor of 909)
...
909 / 908 = 1.0011013215859 (the remainder is 1, so 908 is not a divisor of 909)
909 / 909 = 1 (the remainder is 0, so 909 is a divisor of 909)

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 909 (i.e. 30.149626863363). 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 $\frac{N}{d} = D$ )

909 / 1 = 909 (the remainder is 0, so 1 and 909 are divisors of 909)
909 / 2 = 454.5 (the remainder is 1, so 2 is not a divisor of 909)
909 / 3 = 303 (the remainder is 0, so 3 and 303 are divisors of 909)
...
909 / 29 = 31.344827586207 (the remainder is 10, so 29 is not a divisor of 909)
909 / 30 = 30.3 (the remainder is 9, so 30 is not a divisor of 909)