What are the divisors of 6035?

1, 5, 17, 71, 85, 355, 1207, 6035

There is a total of 8 positive divisors.
The sum of these divisors is 7776.
The arithmetic mean is 972.

8 odd divisors

1, 5, 17, 71, 85, 355, 1207, 6035

How to compute the divisors of 6035?

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 6035 by each of the numbers from 1 to 6035 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)

6035 / 1 = 6035 (the remainder is 0, so 1 is a divisor of 6035)
6035 / 2 = 3017.5 (the remainder is 1, so 2 is not a divisor of 6035)
6035 / 3 = 2011.6666666667 (the remainder is 2, so 3 is not a divisor of 6035)
...
6035 / 6034 = 1.0001657275439 (the remainder is 1, so 6034 is not a divisor of 6035)
6035 / 6035 = 1 (the remainder is 0, so 6035 is a divisor of 6035)

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 6035 (i.e. 77.685262437608). 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 $\frac{N}{d} = D$ )

6035 / 1 = 6035 (the remainder is 0, so 1 and 6035 are divisors of 6035)
6035 / 2 = 3017.5 (the remainder is 1, so 2 is not a divisor of 6035)
6035 / 3 = 2011.6666666667 (the remainder is 2, so 3 is not a divisor of 6035)
...
6035 / 76 = 79.407894736842 (the remainder is 31, so 76 is not a divisor of 6035)
6035 / 77 = 78.376623376623 (the remainder is 29, so 77 is not a divisor of 6035)