What are the divisors of 8035?

1, 5, 1607, 8035

There is a total of 4 positive divisors.
The sum of these divisors is 9648.
The arithmetic mean is 2412.

4 odd divisors

1, 5, 1607, 8035

How to compute the divisors of 8035?

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 8035 by each of the numbers from 1 to 8035 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)

8035 / 1 = 8035 (the remainder is 0, so 1 is a divisor of 8035)
8035 / 2 = 4017.5 (the remainder is 1, so 2 is not a divisor of 8035)
8035 / 3 = 2678.3333333333 (the remainder is 1, so 3 is not a divisor of 8035)
...
8035 / 8034 = 1.0001244709983 (the remainder is 1, so 8034 is not a divisor of 8035)
8035 / 8035 = 1 (the remainder is 0, so 8035 is a divisor of 8035)

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 8035 (i.e. 89.638161516176). 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 $\frac{N}{d} = D$ )

8035 / 1 = 8035 (the remainder is 0, so 1 and 8035 are divisors of 8035)
8035 / 2 = 4017.5 (the remainder is 1, so 2 is not a divisor of 8035)
8035 / 3 = 2678.3333333333 (the remainder is 1, so 3 is not a divisor of 8035)
...
8035 / 88 = 91.306818181818 (the remainder is 27, so 88 is not a divisor of 8035)
8035 / 89 = 90.280898876404 (the remainder is 25, so 89 is not a divisor of 8035)