Question

show that the product of any three consecutive even integers is divisible by 48

Answer 1

let the integers be 2,4,6.
then their product is 48 which is completely divisible by 48.


Hope this works :)

Answer 2

The product of any three consecutive even integers is divisible by 48.

Step-by-step explanation:

Let the  three consecutive even integers = x, (x + 2) and (x + 4)

To prove that, the product of any three consecutive even integers is divisible by 48.

According to question,

x(x + 2)(x + 4) is divisible by 48.

Put x = 2, 4, 6, 8, 10, ......

Put x = 2, we get

2(2 + 2)(2 + 4)

=2(4)(6) =48, is divisible by 48

Put x = 4, we get

4(4 + 2)(4 + 4)

=4(6)(8) =192, is divisible by 48

...

Hence, the product of three consecutive even integers is divisible by 48.