What are the divisors of 1837?

1, 11, 167, 1837

There is a total of 4 positive divisors.
The sum of these divisors is 2016.
The arithmetic mean is 504.

4 odd divisors

1, 11, 167, 1837

How to compute the divisors of 1837?

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 1837 by each of the numbers from 1 to 1837 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)

1837 / 1 = 1837 (the remainder is 0, so 1 is a divisor of 1837)
1837 / 2 = 918.5 (the remainder is 1, so 2 is not a divisor of 1837)
1837 / 3 = 612.33333333333 (the remainder is 1, so 3 is not a divisor of 1837)
...
1837 / 1836 = 1.0005446623094 (the remainder is 1, so 1836 is not a divisor of 1837)
1837 / 1837 = 1 (the remainder is 0, so 1837 is a divisor of 1837)

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 1837 (i.e. 42.860237983474). 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 $\frac{N}{d} = D$ )

1837 / 1 = 1837 (the remainder is 0, so 1 and 1837 are divisors of 1837)
1837 / 2 = 918.5 (the remainder is 1, so 2 is not a divisor of 1837)
1837 / 3 = 612.33333333333 (the remainder is 1, so 3 is not a divisor of 1837)
...
1837 / 41 = 44.80487804878 (the remainder is 33, so 41 is not a divisor of 1837)
1837 / 42 = 43.738095238095 (the remainder is 31, so 42 is not a divisor of 1837)