What are the divisors of 303?

1, 3, 101, 303

There is a total of 4 positive divisors.
The sum of these divisors is 408.
The arithmetic mean is 102.

4 odd divisors

1, 3, 101, 303

How to compute the divisors of 303?

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 303 by each of the numbers from 1 to 303 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)

303 / 1 = 303 (the remainder is 0, so 1 is a divisor of 303)
303 / 2 = 151.5 (the remainder is 1, so 2 is not a divisor of 303)
303 / 3 = 101 (the remainder is 0, so 3 is a divisor of 303)
...
303 / 302 = 1.0033112582781 (the remainder is 1, so 302 is not a divisor of 303)
303 / 303 = 1 (the remainder is 0, so 303 is a divisor of 303)

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 303 (i.e. 17.406895185529). 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 $\frac{N}{d} = D$ )

303 / 1 = 303 (the remainder is 0, so 1 and 303 are divisors of 303)
303 / 2 = 151.5 (the remainder is 1, so 2 is not a divisor of 303)
303 / 3 = 101 (the remainder is 0, so 3 and 101 are divisors of 303)
...
303 / 16 = 18.9375 (the remainder is 15, so 16 is not a divisor of 303)
303 / 17 = 17.823529411765 (the remainder is 14, so 17 is not a divisor of 303)