Math, asked by ritu23mehta, 1 year ago

The product of three consecutive positive integer is divisible by 6.
Is this statement true or false. Justify your answer

Answers

Answered by avni576
12

Let three consecutive positive integers be, n, n + 1 and n + 2. 

When a number is divided by 3, the remainder obtained is either 0 or 1 or 2.  

∴ n = 3p or 3p + 1 or 3p + 2, where p is some integer.

If n = 3p, then n is divisible by 3. 

If n = 3p + 1, ⇒ n + 2 = 3p + 1 + 2 = 3p + 3 = 3(p + 1) is divisible by 3. 

If n = 3p + 2, ⇒ n + 1 = 3p + 2 + 1 = 3p + 3 = 3(p + 1) is divisible by 3. 

 

So, we can say that one of the numbers among n, n + 1 and n + 2 is always divisible by 3.  

⇒ n (n + 1) (n + 2) is divisible by 3. 

 

Similarly, when a number is divided 2, the remainder obtained is 0 or 1. 

∴ n = 2q or 2q + 1, where q is some integer. 

If n = 2q ⇒ n and n + 2 = 2q + 2 = 2(q + 1) are divisible by 2. 

If n = 2q + 1 ⇒ n + 1 = 2q + 1 + 1 = 2q + 2 = 2 (q + 1) is divisible by 2. 

 

So, we can say that one of the numbers among n, n + 1 and n + 2 is always divisible by 2. 

⇒ n (n + 1) (n + 2) is divisible by 2. 

 

Hence n (n + 1) (n + 2) is divisible by 2 and 3.

∴ n (n + 1) (n + 2) is divisible by 6. 


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Answered by riturathee25
4

Answer:

It is true

Let the nos. be 1 , 2 and 3

Their product is divisible by 6

And many more examples may be used

Step-by-step explanation:

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