What are the divisors of 1873?

1, 1873

There is a total of 2 positive divisors.
The sum of these divisors is 1874.
The arithmetic mean is 937.

2 odd divisors

1, 1873

How to compute the divisors of 1873?

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 1873 by each of the numbers from 1 to 1873 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)

1873 / 1 = 1873 (the remainder is 0, so 1 is a divisor of 1873)
1873 / 2 = 936.5 (the remainder is 1, so 2 is not a divisor of 1873)
1873 / 3 = 624.33333333333 (the remainder is 1, so 3 is not a divisor of 1873)
...
1873 / 1872 = 1.0005341880342 (the remainder is 1, so 1872 is not a divisor of 1873)
1873 / 1873 = 1 (the remainder is 0, so 1873 is a divisor of 1873)

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 1873 (i.e. 43.278170016765). 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 $\frac{N}{d} = D$ )

1873 / 1 = 1873 (the remainder is 0, so 1 and 1873 are divisors of 1873)
1873 / 2 = 936.5 (the remainder is 1, so 2 is not a divisor of 1873)
1873 / 3 = 624.33333333333 (the remainder is 1, so 3 is not a divisor of 1873)
...
1873 / 42 = 44.595238095238 (the remainder is 25, so 42 is not a divisor of 1873)
1873 / 43 = 43.558139534884 (the remainder is 24, so 43 is not a divisor of 1873)