- Trending Categories
- Data Structure
- Operating System
- C Programming
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
The product of three consecutive numbers is always divisible by 6 . Verify this statement with the help of some examples.
"Product of three consecutive positive integers is divisible by 6".
We have to find whether the given statement is true or false.
Let three consecutive numbers be $a\ -\ 1$, $a$ and $a\ +\ 1$.
Product $=\ (a\ -\ 1)\ \times\ (a)\ \times\ (a\ +\ 1)$
We know that in any three consecutive numbers:
- One number must be even, and the product is divisible by 2.
- One number must be multiple of 3, and the product is divisible by 3 also.
If a number is divisible by 2 and 3 both then that number is divisible by 6.
Therefore, the product of three consecutive positive integers is divisible by 6.
- Find permutation of n which is divisible by 3 but not divisible by 6 in C++
- Maximum Product of Three Numbers in C++
- Check if product of first N natural numbers is divisible by their sum in Python
- Count pairs of numbers from 1 to N with Product divisible by their Sum in C++
- Number of Substrings divisible by 6 in a String of Integers in C++
- What is the synonym statement of SHOW DATABASES with the help of which we can see the list of MySQL databases?
- Largest N digit number divisible by given three numbers in C++
- Check whether product of digits at even places is divisible by sum of digits at odd place of a numbers in Python
- Greatest Sum Divisible by Three in C++
- Number of Groups of Sizes Two Or Three Divisible By 3 in C++
- Count subarrays whose product is divisible by k in C++
- Program to find number of consecutive subsequences whose sum is divisible by k in Python