How many numbers are there between 1 and 200 | vedclass

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(C) First,find the count of numbers between $1$ and $200$ that are divisible by $3$. This is given by $lfloor 200/3 \rfloor = 66$.Next,identify number

Vedclass · Accepted Answer

$57$

Vedclass · Answer

(C) First,find the count of numbers between $1$ and $200$ that are divisible by $3$. This is given by $lfloor 200/3 floor = 66$.Next,identify numbers that are divisible by both $3$ and $7$. Since $3$ and $7$ are coprime,these are multiples of $	ext{lcm}(3, 7) = 21$.The count of numbers between $1$ and $200$ divisible by $21$ is $lfloor 200/21 floor = 9$.To find the numbers divisible by $3$ but not by $7$,subtract the count of multiples of $21$ from the count of multiples of $3$.Result $= 66 - 9 = 57$.

How many numbers are there between $1$ and $200$ which are divisible by $3$ but not by $7$?

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