What are the divisors of 1853?

1, 17, 109, 1853

There is a total of 4 positive divisors.
The sum of these divisors is 1980.
The arithmetic mean is 495.

4 odd divisors

1, 17, 109, 1853

How to compute the divisors of 1853?

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 1853 by each of the numbers from 1 to 1853 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)

1853 / 1 = 1853 (the remainder is 0, so 1 is a divisor of 1853)
1853 / 2 = 926.5 (the remainder is 1, so 2 is not a divisor of 1853)
1853 / 3 = 617.66666666667 (the remainder is 2, so 3 is not a divisor of 1853)
...
1853 / 1852 = 1.0005399568035 (the remainder is 1, so 1852 is not a divisor of 1853)
1853 / 1853 = 1 (the remainder is 0, so 1853 is a divisor of 1853)

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 1853 (i.e. 43.046486500062). 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 $\frac{N}{d} = D$ )

1853 / 1 = 1853 (the remainder is 0, so 1 and 1853 are divisors of 1853)
1853 / 2 = 926.5 (the remainder is 1, so 2 is not a divisor of 1853)
1853 / 3 = 617.66666666667 (the remainder is 2, so 3 is not a divisor of 1853)
...
1853 / 42 = 44.119047619048 (the remainder is 5, so 42 is not a divisor of 1853)
1853 / 43 = 43.093023255814 (the remainder is 4, so 43 is not a divisor of 1853)