What are the divisors of 1889?

1, 1889

There is a total of 2 positive divisors.
The sum of these divisors is 1890.
The arithmetic mean is 945.

2 odd divisors

1, 1889

How to compute the divisors of 1889?

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 1889 by each of the numbers from 1 to 1889 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)

1889 / 1 = 1889 (the remainder is 0, so 1 is a divisor of 1889)
1889 / 2 = 944.5 (the remainder is 1, so 2 is not a divisor of 1889)
1889 / 3 = 629.66666666667 (the remainder is 2, so 3 is not a divisor of 1889)
...
1889 / 1888 = 1.0005296610169 (the remainder is 1, so 1888 is not a divisor of 1889)
1889 / 1889 = 1 (the remainder is 0, so 1889 is a divisor of 1889)

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 1889 (i.e. 43.462627624201). 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 $\frac{N}{d} = D$ )

1889 / 1 = 1889 (the remainder is 0, so 1 and 1889 are divisors of 1889)
1889 / 2 = 944.5 (the remainder is 1, so 2 is not a divisor of 1889)
1889 / 3 = 629.66666666667 (the remainder is 2, so 3 is not a divisor of 1889)
...
1889 / 42 = 44.97619047619 (the remainder is 41, so 42 is not a divisor of 1889)
1889 / 43 = 43.93023255814 (the remainder is 40, so 43 is not a divisor of 1889)