What are the divisors of 1849?

1, 43, 1849

There is a total of 3 positive divisors.
The sum of these divisors is 1893.
The arithmetic mean is 631.

3 odd divisors

1, 43, 1849

How to compute the divisors of 1849?

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 1849 by each of the numbers from 1 to 1849 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)

1849 / 1 = 1849 (the remainder is 0, so 1 is a divisor of 1849)
1849 / 2 = 924.5 (the remainder is 1, so 2 is not a divisor of 1849)
1849 / 3 = 616.33333333333 (the remainder is 1, so 3 is not a divisor of 1849)
...
1849 / 1848 = 1.0005411255411 (the remainder is 1, so 1848 is not a divisor of 1849)
1849 / 1849 = 1 (the remainder is 0, so 1849 is a divisor of 1849)

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 1849 (i.e. 43). 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 $\frac{N}{d} = D$ )

1849 / 1 = 1849 (the remainder is 0, so 1 and 1849 are divisors of 1849)
1849 / 2 = 924.5 (the remainder is 1, so 2 is not a divisor of 1849)
1849 / 3 = 616.33333333333 (the remainder is 1, so 3 is not a divisor of 1849)
...
1849 / 42 = 44.02380952381 (the remainder is 1, so 42 is not a divisor of 1849)
1849 / 43 = 43 (the remainder is 0, so 43 and 43 are divisors of 1849)