What are the divisors of 6038?

1, 2, 3019, 6038

There is a total of 4 positive divisors.
The sum of these divisors is 9060.
The arithmetic mean is 2265.

2 even divisors

2, 6038

2 odd divisors

1, 3019

How to compute the divisors of 6038?

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 6038 by each of the numbers from 1 to 6038 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)

6038 / 1 = 6038 (the remainder is 0, so 1 is a divisor of 6038)
6038 / 2 = 3019 (the remainder is 0, so 2 is a divisor of 6038)
6038 / 3 = 2012.6666666667 (the remainder is 2, so 3 is not a divisor of 6038)
...
6038 / 6037 = 1.000165645188 (the remainder is 1, so 6037 is not a divisor of 6038)
6038 / 6038 = 1 (the remainder is 0, so 6038 is a divisor of 6038)

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 6038 (i.e. 77.70456872025). 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 $\frac{N}{d} = D$ )

6038 / 1 = 6038 (the remainder is 0, so 1 and 6038 are divisors of 6038)
6038 / 2 = 3019 (the remainder is 0, so 2 and 3019 are divisors of 6038)
6038 / 3 = 2012.6666666667 (the remainder is 2, so 3 is not a divisor of 6038)
...
6038 / 76 = 79.447368421053 (the remainder is 34, so 76 is not a divisor of 6038)
6038 / 77 = 78.415584415584 (the remainder is 32, so 77 is not a divisor of 6038)