Question

The product of three consecutive number is always divisible by
a)2
(b)4
(c) 6
d)8
​

Answer 1

1×2×3=6

is divisible by 2

6×7×8=336 it 8a also divisible by 2

so, the answer is

a)2

Answer 2

Answer:

6

Step-by-step explanation:

using trial and error take smallest three consecutive no. 1*2*3 is divisible by 6

also 2*3*4 divisible by 6

3*4*5 divisible by 6

OR

as we know that three consecutive no will be of the for let n , n+1,n+2

then as we can see that it can have at least one even no. hense it will be

divisible by 2 also

Whenever a number is divided by 3, the remainder obtained is either 0,1 or 2.Therefore, 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, then n+2=3p+1+2=3p+3=3(p+1) is divisible by 3.

If n=3p+2, then 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 that is:

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