Question

the product of three consecutive numbers is always divisivble by 6 . verify this statements with the help of some examples​

Answer 1

Step-by-step explanation:

We know that a number is divisible by 6, if the number is divisible by both 2 and 3

example 1: let the three consecutive numbers be 7,8 and 9.

product of numbers

7\times8\times9=5047×8×9=504

units digit of the 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 both 2 and 3 so 504 is divisible by 6.

hence verified.

Answer 2

Step-by-step explanation:

It is stated that "The product of three consecutive number is always divisible by 6." We've been asked to verify this statement with the help of some examples.

1) Let the three consecutive numbers be 2, 3, and 4. Now, let us find the product of the three consecutive numbers.

$\twoheadrightarrow\quad\sf{Product=2\times 3\times 4}$

Performing multiplication.

$\twoheadrightarrow\quad\sf{Product=24}$

Here, we have calculated the product of three consecutive numbers (2, 3 and 4) which is divisible by 6.

2) Let the three consecutive numbers be 5, 6 and 7. Now, let us find the product of the three consecutive numbers.

$\twoheadrightarrow\quad\sf{Product=5\times 6\times 7}$

Performing multiplication.

$\twoheadrightarrow\quad\sf{Product=210}$

Here, we have calculated the product of three consecutive numbers (5, 6 and 7) which is divisible by 6.

3) Let the three consecutive numbers be 8, 9 and 10. Now, let us find the product of three consecutive numbers.

$\twoheadrightarrow\quad\sf{Product=8\times 9\times 10}$

Performing multiplication.

$\twoheadrightarrow\quad\sf{Product=720}$

Here, we have calculated the product of three consecutive numbers (8, 9 and 10) which is divisible by 6.

Henceforth, the statement "Product of three consecutive numbers is always divisible by 6" is verified.