What are the divisors of 6092?

1, 2, 4, 1523, 3046, 6092

There is a total of 6 positive divisors.
The sum of these divisors is 10668.
The arithmetic mean is 1778.

4 even divisors

2, 4, 3046, 6092

2 odd divisors

1, 1523

How to compute the divisors of 6092?

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 6092 by each of the numbers from 1 to 6092 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)

6092 / 1 = 6092 (the remainder is 0, so 1 is a divisor of 6092)
6092 / 2 = 3046 (the remainder is 0, so 2 is a divisor of 6092)
6092 / 3 = 2030.6666666667 (the remainder is 2, so 3 is not a divisor of 6092)
...
6092 / 6091 = 1.0001641766541 (the remainder is 1, so 6091 is not a divisor of 6092)
6092 / 6092 = 1 (the remainder is 0, so 6092 is a divisor of 6092)

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 6092 (i.e. 78.051265204351). 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 $\frac{N}{d} = D$ )

6092 / 1 = 6092 (the remainder is 0, so 1 and 6092 are divisors of 6092)
6092 / 2 = 3046 (the remainder is 0, so 2 and 3046 are divisors of 6092)
6092 / 3 = 2030.6666666667 (the remainder is 2, so 3 is not a divisor of 6092)
...
6092 / 77 = 79.116883116883 (the remainder is 9, so 77 is not a divisor of 6092)
6092 / 78 = 78.102564102564 (the remainder is 8, so 78 is not a divisor of 6092)