What are the divisors of 933?

1, 3, 311, 933

There is a total of 4 positive divisors.
The sum of these divisors is 1248.
The arithmetic mean is 312.

4 odd divisors

1, 3, 311, 933

How to compute the divisors of 933?

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 933 by each of the numbers from 1 to 933 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)

933 / 1 = 933 (the remainder is 0, so 1 is a divisor of 933)
933 / 2 = 466.5 (the remainder is 1, so 2 is not a divisor of 933)
933 / 3 = 311 (the remainder is 0, so 3 is a divisor of 933)
...
933 / 932 = 1.0010729613734 (the remainder is 1, so 932 is not a divisor of 933)
933 / 933 = 1 (the remainder is 0, so 933 is a divisor of 933)

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 933 (i.e. 30.545048698603). 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 $\frac{N}{d} = D$ )

933 / 1 = 933 (the remainder is 0, so 1 and 933 are divisors of 933)
933 / 2 = 466.5 (the remainder is 1, so 2 is not a divisor of 933)
933 / 3 = 311 (the remainder is 0, so 3 and 311 are divisors of 933)
...
933 / 29 = 32.172413793103 (the remainder is 5, so 29 is not a divisor of 933)
933 / 30 = 31.1 (the remainder is 3, so 30 is not a divisor of 933)