What are the divisors of 1923?

1, 3, 641, 1923

There is a total of 4 positive divisors.
The sum of these divisors is 2568.
The arithmetic mean is 642.

4 odd divisors

1, 3, 641, 1923

How to compute the divisors of 1923?

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 1923 by each of the numbers from 1 to 1923 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)

1923 / 1 = 1923 (the remainder is 0, so 1 is a divisor of 1923)
1923 / 2 = 961.5 (the remainder is 1, so 2 is not a divisor of 1923)
1923 / 3 = 641 (the remainder is 0, so 3 is a divisor of 1923)
...
1923 / 1922 = 1.0005202913632 (the remainder is 1, so 1922 is not a divisor of 1923)
1923 / 1923 = 1 (the remainder is 0, so 1923 is a divisor of 1923)

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 1923 (i.e. 43.852023898561). 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 $\frac{N}{d} = D$ )

1923 / 1 = 1923 (the remainder is 0, so 1 and 1923 are divisors of 1923)
1923 / 2 = 961.5 (the remainder is 1, so 2 is not a divisor of 1923)
1923 / 3 = 641 (the remainder is 0, so 3 and 641 are divisors of 1923)
...
1923 / 42 = 45.785714285714 (the remainder is 33, so 42 is not a divisor of 1923)
1923 / 43 = 44.720930232558 (the remainder is 31, so 43 is not a divisor of 1923)