Question

1.) which actual division,find whether the rational number 1323/6power3*35power2 has a terminating or a non terminating decimal.
2.) show that the product of three consecutive natural number is divisible by 6.

Answer 1

2 for example let's take 2,3,4 as three consecutive numbers so 2*3*4 =24 which is divisible by 6. Another ex. 7*8*9 = 504 which is divisible by 6.

Answer 2

Given 1323/63*352 

= 1323/23x33 x 72x52 


∴ It is terminating desimal.Because of it is not in the form of 2m5n

Suppose n is a natural number, such that the 3 consecutive natural numbers is n,n+1,n+2. Then,

n(n+1)(n+2)6=1(1+1)(1+2)6=66=1 Thus, n(n+1)(n+2) is divisble by 6.