What are the divisors of 903?

1, 3, 7, 21, 43, 129, 301, 903

There is a total of 8 positive divisors.
The sum of these divisors is 1408.
The arithmetic mean is 176.

8 odd divisors

1, 3, 7, 21, 43, 129, 301, 903

How to compute the divisors of 903?

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 903 by each of the numbers from 1 to 903 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)

903 / 1 = 903 (the remainder is 0, so 1 is a divisor of 903)
903 / 2 = 451.5 (the remainder is 1, so 2 is not a divisor of 903)
903 / 3 = 301 (the remainder is 0, so 3 is a divisor of 903)
...
903 / 902 = 1.0011086474501 (the remainder is 1, so 902 is not a divisor of 903)
903 / 903 = 1 (the remainder is 0, so 903 is a divisor of 903)

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 903 (i.e. 30.049958402633). 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 $\frac{N}{d} = D$ )

903 / 1 = 903 (the remainder is 0, so 1 and 903 are divisors of 903)
903 / 2 = 451.5 (the remainder is 1, so 2 is not a divisor of 903)
903 / 3 = 301 (the remainder is 0, so 3 and 301 are divisors of 903)
...
903 / 29 = 31.137931034483 (the remainder is 4, so 29 is not a divisor of 903)
903 / 30 = 30.1 (the remainder is 3, so 30 is not a divisor of 903)