Is it true that the product of three consecutive numbers is always divisible by 6?

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

The given number is 6.
When any number is divisible by 2 and 3, then this number is divisible by 6 also.
The numbers ending with 0, 2, 4, 6, or 8 are divisible by 2 and if the sum of numbers are divisible by 3, then the number is also divisible by 3.
Multiply the three consecutive numbers,
2 × 3 × 4 = 24
Since the number 24 ends with 0, it is divisible by 2.
Now, adding the digits of 24:
2+4=6
As we can see, 6 is divisible 3. Hence, the product of three consecutive numbers is divisible by 6 and thus the given statement is true.
Therefore, option 1 is correct.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th