What are the divisors of 2035?

1, 5, 11, 37, 55, 185, 407, 2035

There is a total of 8 positive divisors.
The sum of these divisors is 2736.
The arithmetic mean is 342.

8 odd divisors

1, 5, 11, 37, 55, 185, 407, 2035

How to compute the divisors of 2035?

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 2035 by each of the numbers from 1 to 2035 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)

2035 / 1 = 2035 (the remainder is 0, so 1 is a divisor of 2035)
2035 / 2 = 1017.5 (the remainder is 1, so 2 is not a divisor of 2035)
2035 / 3 = 678.33333333333 (the remainder is 1, so 3 is not a divisor of 2035)
...
2035 / 2034 = 1.0004916420846 (the remainder is 1, so 2034 is not a divisor of 2035)
2035 / 2035 = 1 (the remainder is 0, so 2035 is a divisor of 2035)

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 2035 (i.e. 45.11097427456). 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 $\frac{N}{d} = D$ )

2035 / 1 = 2035 (the remainder is 0, so 1 and 2035 are divisors of 2035)
2035 / 2 = 1017.5 (the remainder is 1, so 2 is not a divisor of 2035)
2035 / 3 = 678.33333333333 (the remainder is 1, so 3 is not a divisor of 2035)
...
2035 / 44 = 46.25 (the remainder is 11, so 44 is not a divisor of 2035)
2035 / 45 = 45.222222222222 (the remainder is 10, so 45 is not a divisor of 2035)