Question

The product of 4 consecutive natural numbers is 5040. Find those numbers.

Answer 1

Form an equation like this. Firstly, those natural numbers would be x,x+1,x+2,x+3

\(\Large \color{MidnightBlue}{\Rightarrow x(x + 1)(x + 2)(x + 3) = 5040}\)

Answer 2

\[5040 = 2^4\times 3^2\times 5\times 7 \]

It should be obvious that 10 is one of them, apparently \(7\times 8\times 9 \times 10 =5040\)

\[7,8,9,10 \]

Answer 3

But how 10?

Answer 4

After you break it up into primes, there is only one 5 and the last digit is 0 hence one number could be 10,20,40, among which 10 is the only logical choice considering the other primes.

Answer 5

Ahh nice :)

Answer 6

Thank you "Parth" and "Fool for Math". I appreciate your sparing time for me.

thank you again.

Answer 7

:)