Aptitude 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.**

**Bharath**

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**Sarah**

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Thanks for the solution!!

**Rajiv Chaudhary**

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Can u explain this solution from start

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.

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

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

**Vishnu Narayan Panday**

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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**

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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

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..