Question

The product of three consecutive numbers always divisible by 6. verify the correctness of the statement with example​

Answer 1

Answer:

pick any three consecutive numbers.

One of them will be divisible by 3 (as we’re talking about 3 consecutive numbers), and at least one of them will be divisible by 2 (as for any 2 consecutive numbers, one will be even, and the other odd). For example

11 12 13 ← example of the number divisible by 3 not an even number

if the even number is divisible by 3, the number will be divisible by 6, and the multiplication with other numbers will still give a result divisible by 6

11*12*13 = 11*(6*2)*13 = 11*6*2*13 = 6*2*11*13

8 9 10 ← example of the number divisible by 3 not an even number

you can write one of the even numbers as twice its half, and the number divisible by 3 as 3 times its third

2*4 3*3 10

when you multiply all these numbers you can take the 2 and 3 together to form 6, and thus the result will be divisible by 6

8*9*10 = (2*4)*(3*3)*10 = 2*4*3*3*10 = (2*3)*4*3*10 = 6*3*4*10