Question

The product of three consuctive numbers is always divicbke by 6.verify this statement with some examples

Answer 1

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

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Answer 2

■QUESTION

The product of three consuctive numbers is always divicbke by 6

■ANSWER

Complete step by step solution:

In the given question, we have to prove that the product of any three consecutive numbers is divisible by 

66

. If a number is divisible by 

66

, then it means that it is also divisible by 

22

 and 

33

.

So, let us prove that the product of any three consecutive numbers is divisible by 

22

 and 

33

.

Consider the three consecutive numbers to be 

x,(x+1),(x+2)x,(x+1),(x+2)

.

For 

22 If xx

 is not divisible by 

22

, then it means that 

xx

 is odd.

Hence, if 

x

 is odd, then it is a known fact that 

x+1x+1

 (any odd number plus 11 )

is even, hence, is divisible by 22

Thus, out of the three consecutive numbers, at least one of them is always divisible by 

22For 33

:

Now, if a number is not divisible by 

33

 and is divided by it, then it can leave either of only two remainder – 

11