What are the divisors of 6034?

1, 2, 7, 14, 431, 862, 3017, 6034

There is a total of 8 positive divisors.
The sum of these divisors is 10368.
The arithmetic mean is 1296.

4 even divisors

2, 14, 862, 6034

4 odd divisors

1, 7, 431, 3017

How to compute the divisors of 6034?

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 6034 by each of the numbers from 1 to 6034 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)

6034 / 1 = 6034 (the remainder is 0, so 1 is a divisor of 6034)
6034 / 2 = 3017 (the remainder is 0, so 2 is a divisor of 6034)
6034 / 3 = 2011.3333333333 (the remainder is 1, so 3 is not a divisor of 6034)
...
6034 / 6033 = 1.0001657550141 (the remainder is 1, so 6033 is not a divisor of 6034)
6034 / 6034 = 1 (the remainder is 0, so 6034 is a divisor of 6034)

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 6034 (i.e. 77.678825943754). 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 $\frac{N}{d} = D$ )

6034 / 1 = 6034 (the remainder is 0, so 1 and 6034 are divisors of 6034)
6034 / 2 = 3017 (the remainder is 0, so 2 and 3017 are divisors of 6034)
6034 / 3 = 2011.3333333333 (the remainder is 1, so 3 is not a divisor of 6034)
...
6034 / 76 = 79.394736842105 (the remainder is 30, so 76 is not a divisor of 6034)
6034 / 77 = 78.363636363636 (the remainder is 28, so 77 is not a divisor of 6034)