What are the divisors of 1894?

1, 2, 947, 1894

There is a total of 4 positive divisors.
The sum of these divisors is 2844.
The arithmetic mean is 711.

2 even divisors

2, 1894

2 odd divisors

1, 947

How to compute the divisors of 1894?

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 1894 by each of the numbers from 1 to 1894 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)

1894 / 1 = 1894 (the remainder is 0, so 1 is a divisor of 1894)
1894 / 2 = 947 (the remainder is 0, so 2 is a divisor of 1894)
1894 / 3 = 631.33333333333 (the remainder is 1, so 3 is not a divisor of 1894)
...
1894 / 1893 = 1.000528262018 (the remainder is 1, so 1893 is not a divisor of 1894)
1894 / 1894 = 1 (the remainder is 0, so 1894 is a divisor of 1894)

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 1894 (i.e. 43.520110293978). 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 $\frac{N}{d} = D$ )

1894 / 1 = 1894 (the remainder is 0, so 1 and 1894 are divisors of 1894)
1894 / 2 = 947 (the remainder is 0, so 2 and 947 are divisors of 1894)
1894 / 3 = 631.33333333333 (the remainder is 1, so 3 is not a divisor of 1894)
...
1894 / 42 = 45.095238095238 (the remainder is 4, so 42 is not a divisor of 1894)
1894 / 43 = 44.046511627907 (the remainder is 2, so 43 is not a divisor of 1894)