# Moderate Number System Solved QuestionAptitude Discussion

 Q. The product of 4 consecutive even numbers is always divisible by:
 ✖ A. 600 ✖ B. 768 ✖ C. 864 ✔ D. 384

Solution:
Option(D) is correct

To solve this question, we need to know two facts.

Fact 1:
The product of 4 consecutive numbers is always divisible by 4!.

Fact 2:
Since, we have 4 even numbers, we have an additional 2 available with each number.

Now, using both the facts, we can say that the product of 4 consecutive even numbers is always divisible by,

$=(2^4) \times 4!$

$= 16 \times 24$

$=\textbf{384}$

Edit: Than you Joe for explaining fact 1 in the comments.

Edit 2: For an alternative solution, check comment by Gopal.

## (9) Comment(s)

Saurabh Gupta
()

Above question is technically wrong ! 0 is also an even number and that will make the product of the four numbers to be zero too and that's not divisible by "384" ! So you must say "four consecutive natural even numbers !" in the questions !

Bharath
()

read the question it can be solved by 4 consecutive even numbers 2 4 6 8 just u multiply them u get the perfect answer..

Sarah
()

Thanks for the solution!!

Rajiv Chaudhary
()

Can u explain this solution from start

Joe
()

it's pretty easy.

I guess you want to know fact 1 presented in the solution (The product of 4 consecutive numbers is always divisible by $4!=24$.)

$24=2 \times 2 \times 2 \times 3$

So you need 3, 2's and a single 3.

if you take and 3 consecutive number,you will have one of them being a multiple of 3.

also,among any 4 consecutive numbers 2 will be even numbers,one of them being a multiple of 4.so you have 3, 2's.

Saif
()

i did't get this concept. can u explain again?

Shireesh
()

Which part needs the explanation? If you elaborate more then maybe I can be of some help.

Vishnu Narayan Panday
()

if we check the divisibility by consecutive 4 even no are (2,4,6,8)

then 384 is divisible by 2,4,6,8

Gopal
()

consecutive 4 even no are

2,4,6,8

take l.c.m for

600

768

864

384

only 384 has 4 consecutive no 2,4,6,8