Is it true that the product of three consecutive natural numbers are always divisible by 6? justify
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True. Suppose n is a natural number, such that the 3 consecutive natural numbers is n,n+1,n+2n,n+1,n+2. Then,
n(n+1)(n+2)6=1(1+1)(1+2)6=66=1n(n+1)(n+2)6=1(1+1)(1+2)6=66=1
Thus, n(n+1)(n+2)n(n+1)(n+2) is divisble by 6.
n(n+1)(n+2)6=1(1+1)(1+2)6=66=1n(n+1)(n+2)6=1(1+1)(1+2)6=66=1
Thus, n(n+1)(n+2)n(n+1)(n+2) is divisble by 6.
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