What are the divisors of 1892?

1, 2, 4, 11, 22, 43, 44, 86, 172, 473, 946, 1892

There is a total of 12 positive divisors.
The sum of these divisors is 3696.
The arithmetic mean is 308.

8 even divisors

2, 4, 22, 44, 86, 172, 946, 1892

4 odd divisors

1, 11, 43, 473

How to compute the divisors of 1892?

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 1892 by each of the numbers from 1 to 1892 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)

1892 / 1 = 1892 (the remainder is 0, so 1 is a divisor of 1892)
1892 / 2 = 946 (the remainder is 0, so 2 is a divisor of 1892)
1892 / 3 = 630.66666666667 (the remainder is 2, so 3 is not a divisor of 1892)
...
1892 / 1891 = 1.0005288207298 (the remainder is 1, so 1891 is not a divisor of 1892)
1892 / 1892 = 1 (the remainder is 0, so 1892 is a divisor of 1892)

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 1892 (i.e. 43.497126341863). 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 $\frac{N}{d} = D$ )

1892 / 1 = 1892 (the remainder is 0, so 1 and 1892 are divisors of 1892)
1892 / 2 = 946 (the remainder is 0, so 2 and 946 are divisors of 1892)
1892 / 3 = 630.66666666667 (the remainder is 2, so 3 is not a divisor of 1892)
...
1892 / 42 = 45.047619047619 (the remainder is 2, so 42 is not a divisor of 1892)
1892 / 43 = 44 (the remainder is 0, so 43 and 44 are divisors of 1892)