Question

The product of four consecutive positive numbers is $840$. Find the numbers.

Answer 1

First we find the prime factors of $840$
$840=2\times 2\times 2\times 3\times 5\times 7$
As you can see we have $5$ and $7$
If we somehow produce a $6$ in between, we'll have 3 consecutive numbers.
Use $2\times 3$ to get $6$ from the expansion of $840$ above we'll be left with $2\times 2$ only.
And $2\times 2=4$
Thus, the 4 consecutive numbers will be $4,5,6$ and $7$ whose product is $840$.