Question

How many numbers up to 200 are divisible by 2 and 3 both?

Answer 1

Numbers divisible by both 2 and 3:
6,12,18,24,…………………………,198
Clearly this is an arithmetical progression, whose first term is 6 and last term is 198
Hence, First term a=6; common difference d=6; nth term T(n)= 198
We know that, in an arithmetic series
T(n)=a+(n-1)d
198=6+(n-1)6
or, [198–6]/6 = n-1
or, 192/6 = n-1
or, 32 = n-1
or, 32+1 = n
or, n= 33

Thus, there are 33 numbers between 1 and 200 which are divisible by both 2 and 3.