What are the divisors of 1893?

1, 3, 631, 1893

There is a total of 4 positive divisors.
The sum of these divisors is 2528.
The arithmetic mean is 632.

4 odd divisors

1, 3, 631, 1893

How to compute the divisors of 1893?

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 1893 by each of the numbers from 1 to 1893 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)

1893 / 1 = 1893 (the remainder is 0, so 1 is a divisor of 1893)
1893 / 2 = 946.5 (the remainder is 1, so 2 is not a divisor of 1893)
1893 / 3 = 631 (the remainder is 0, so 3 is a divisor of 1893)
...
1893 / 1892 = 1.0005285412262 (the remainder is 1, so 1892 is not a divisor of 1893)
1893 / 1893 = 1 (the remainder is 0, so 1893 is a divisor of 1893)

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 1893 (i.e. 43.508619835614). 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 $\frac{N}{d} = D$ )

1893 / 1 = 1893 (the remainder is 0, so 1 and 1893 are divisors of 1893)
1893 / 2 = 946.5 (the remainder is 1, so 2 is not a divisor of 1893)
1893 / 3 = 631 (the remainder is 0, so 3 and 631 are divisors of 1893)
...
1893 / 42 = 45.071428571429 (the remainder is 3, so 42 is not a divisor of 1893)
1893 / 43 = 44.023255813953 (the remainder is 1, so 43 is not a divisor of 1893)