number theory - Partitioning integers into sets

Try to find out if it is possible to partition 6 consecutive positive integers into two sets, $A_1$ and $A_2$ such that the product of the elements in $A_1$ is equal to the product of the elements in $A_2$?

Also, check if this is possible for 20 consecutive positive integers?

I said:

Let $K=$ positive integer, then we need to partition:

$$K, K+1, K+2, K+3, K+4, K+5 $$

This wasnt helping me so i worked with numbers.

I started out with:

$$ 1,2,3,4,5,6 $$

and i can't seem to partition it.

So i worked with:

$$ 2,3,4,5,6,7 $$

I tried:

$A_1=4,7,3=84$
$A_2=2,5,6=60$

and I tried more cases but trial and error does not seem to be effective. Any strategies or patterns anybody else notice?