Question

Is it true that the product of 3 consecutive natural number is always divisible by 6? Justify your answer.

Answer 1

Answer:Yes

Step-by-step explanation

Let assume 3,4,5

3×4×5 = 60

It is divisible by 6

Answer 2

Let's assume a natural number 'n' which is not divisible by 2 or 3.

Thus, n is an odd number.

The numbers after n will be (n+1) and (n+2).

Now, (n+1) ,ust be an even number as it is just after an odd number n.

so, it'll be divisible by 2.

(n+1) = 2.k

Now, as n is not divisible by 3, (n+2) must be.

Between any 2 consecutive numbers divisible by 3, the maximum gap is 2.

Like, 3 and 6- inbetween 4 & 5. It's simply because in natural number series every 3 multiple position number will be divisible by three.

So, it (n+2) can be written as 3.m

(n+2) = 3.m

Now,

n(n+1)(n+2) = n.2k.3m = 6nkm

It's divisible by 6.