Home
Class 10
MATHS
The product of any three consecutive ...

The product of any three consecutive natural numbers is divisible by 6 (True/false).

Text Solution

AI Generated Solution

To determine whether the product of any three consecutive natural numbers is divisible by 6, we can follow these steps: ### Step 1: Define the three consecutive natural numbers Let the three consecutive natural numbers be represented as: - \( n \) - \( n + 1 \) - \( n + 2 \) ...
Promotional Banner

Topper's Solved these Questions

  • REAL NUMBERS

    NCERT EXEMPLAR ENGLISH|Exercise SHORT ANSWER TYPE QUESTIONS|14 Videos

  • REAL NUMBERS

    NCERT EXEMPLAR ENGLISH|Exercise LONG ANSWER TYPE QUESTIONS|5 Videos

  • REAL NUMBERS

    NCERT EXEMPLAR ENGLISH|Exercise LONG ANSWER TYPE QUESTIONS|5 Videos

  • QUADRIATIC EQUATIONS

    NCERT EXEMPLAR ENGLISH|Exercise LONG ANSWER TYPE|12 Videos

  • STATISTICS AND PROBABILITY

    NCERT EXEMPLAR ENGLISH|Exercise LONG ASWERS QUESTIONS|14 Videos

Similar Questions

Explore conceptually related problems

The product of n consecutive natural numbers is always divisible by

Statement-1: n(n+1)(n+2) is always divisible by 6 for all n in N . Statement-2: The product of any two consecutive natural number is divisible by 2.

True or false: The product of any r consecutive natural numbers is always divisible by r!

The sum of the cubes of three consecutive natural numbers is divisible by

Prove by induction that the sum of the cubes of three consecutive natural numbers is divisible by 9.

The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples.

Show that product of any n consecutive integers is always divisible by n!

Prove that the product of three consecutive positive integers is divisible by 6 .

Property:Product of r consecutive number is divisible by r!

Statement-1: The smallest positive integer n such that n! can be expressed as a product of n-3 consecutive integers, is 6. Statement-2: Product of three consecutive integers is divisible by 6.