What are the divisors of 6029?

1, 6029

There is a total of 2 positive divisors.
The sum of these divisors is 6030.
The arithmetic mean is 3015.

2 odd divisors

1, 6029

How to compute the divisors of 6029?

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 6029 by each of the numbers from 1 to 6029 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)

6029 / 1 = 6029 (the remainder is 0, so 1 is a divisor of 6029)
6029 / 2 = 3014.5 (the remainder is 1, so 2 is not a divisor of 6029)
6029 / 3 = 2009.6666666667 (the remainder is 2, so 3 is not a divisor of 6029)
...
6029 / 6028 = 1.0001658925017 (the remainder is 1, so 6028 is not a divisor of 6029)
6029 / 6029 = 1 (the remainder is 0, so 6029 is a divisor of 6029)

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 6029 (i.e. 77.646635471217). 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 $\frac{N}{d} = D$ )

6029 / 1 = 6029 (the remainder is 0, so 1 and 6029 are divisors of 6029)
6029 / 2 = 3014.5 (the remainder is 1, so 2 is not a divisor of 6029)
6029 / 3 = 2009.6666666667 (the remainder is 2, so 3 is not a divisor of 6029)
...
6029 / 76 = 79.328947368421 (the remainder is 25, so 76 is not a divisor of 6029)
6029 / 77 = 78.298701298701 (the remainder is 23, so 77 is not a divisor of 6029)