question_answer 1)

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

Answer:

                We know that, a number is divisible by 6, if the number is divisible by 2 and 3 both. Example 1 Let the three consecutive numbers be 7, 8 and 9. Product of numbers \[=7\times 8\times 9=504\] Units digit of number = 4, so it is divisible by 2. Now, sum of the digit = 5 + 0 + 4 = 9, which is a multiple of 3. So, 504 is divisible by 3. \[\because \] 504 is divisible by both 2 and 3, so 504 is divisible by 6. Example 2 Let the three consecutive numbers be 11, 12 and 13. Product of numbers \[=11\times 12\times 13=1716\] Units digit of number = 6, so it is divisible by 2. Now, sum of the digit = 1 + 7 + 1 + 6 = 15, which is a multiple of 3. So, 1716 is divisible by 3. \[\because \] 1716 is divisible by both 2 and 3. \[\therefore \] 1716 is divisible by 6.                    Hence, verified.