Question

The product of any three consecutive natural number is divisible by

Answer 1

Answer:

If you have 3 consecutive natural numbers, then at least 1 of them must be divisible by 2, and 1 of them must be divisible by 3. Thus their product must always be divisible by 2x3=6.

Answer 2

Step-by-step explanation:

Let n,n+1,n+2 be three consecutive natural numbers and P (n) be their product. Then,

P(n)=n(n+1)(n+2)

We have,

P(1)=1×2×3=6, which is divisible by 3 and 6.

P(2)=2×3×4=24, which is divisible by 3, 8 and 6.

P(3)=3×4×5=60, which is divisible by 3 and 6.

P(4)=4×5×6=120, which is divisible by 3, 8 and 6.

Hence, P(n) is divisible by 3 and 6 for all  n∈ N.