What are the divisors of 1851?

1, 3, 617, 1851

There is a total of 4 positive divisors.
The sum of these divisors is 2472.
The arithmetic mean is 618.

4 odd divisors

1, 3, 617, 1851

How to compute the divisors of 1851?

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 1851 by each of the numbers from 1 to 1851 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)

1851 / 1 = 1851 (the remainder is 0, so 1 is a divisor of 1851)
1851 / 2 = 925.5 (the remainder is 1, so 2 is not a divisor of 1851)
1851 / 3 = 617 (the remainder is 0, so 3 is a divisor of 1851)
...
1851 / 1850 = 1.0005405405405 (the remainder is 1, so 1850 is not a divisor of 1851)
1851 / 1851 = 1 (the remainder is 0, so 1851 is a divisor of 1851)

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 1851 (i.e. 43.023249528598). 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 $\frac{N}{d} = D$ )

1851 / 1 = 1851 (the remainder is 0, so 1 and 1851 are divisors of 1851)
1851 / 2 = 925.5 (the remainder is 1, so 2 is not a divisor of 1851)
1851 / 3 = 617 (the remainder is 0, so 3 and 617 are divisors of 1851)
...
1851 / 42 = 44.071428571429 (the remainder is 3, so 42 is not a divisor of 1851)
1851 / 43 = 43.046511627907 (the remainder is 2, so 43 is not a divisor of 1851)