What are the divisors of 6028?

1, 2, 4, 11, 22, 44, 137, 274, 548, 1507, 3014, 6028

There is a total of 12 positive divisors.
The sum of these divisors is 11592.
The arithmetic mean is 966.

8 even divisors

2, 4, 22, 44, 274, 548, 3014, 6028

4 odd divisors

1, 11, 137, 1507

How to compute the divisors of 6028?

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 6028 by each of the numbers from 1 to 6028 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)

6028 / 1 = 6028 (the remainder is 0, so 1 is a divisor of 6028)
6028 / 2 = 3014 (the remainder is 0, so 2 is a divisor of 6028)
6028 / 3 = 2009.3333333333 (the remainder is 1, so 3 is not a divisor of 6028)
...
6028 / 6027 = 1.0001659200265 (the remainder is 1, so 6027 is not a divisor of 6028)
6028 / 6028 = 1 (the remainder is 0, so 6028 is a divisor of 6028)

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 6028 (i.e. 77.640195775127). 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 $\frac{N}{d} = D$ )

6028 / 1 = 6028 (the remainder is 0, so 1 and 6028 are divisors of 6028)
6028 / 2 = 3014 (the remainder is 0, so 2 and 3014 are divisors of 6028)
6028 / 3 = 2009.3333333333 (the remainder is 1, so 3 is not a divisor of 6028)
...
6028 / 76 = 79.315789473684 (the remainder is 24, so 76 is not a divisor of 6028)
6028 / 77 = 78.285714285714 (the remainder is 22, so 77 is not a divisor of 6028)