Question

Find the number of numbers between 170 and 320 which are divisible by both 2 and 3 .​

Answer 1

SOLUTION

TO DETERMINE

The number of numbers between 170 and 320 which are divisible by both 2 and 3

EVALUATION

We have to find the number of numbers between 170 and 320 which are divisible by both 2 and 3

If a number is divisible by both 2 & 3 then it is also divisible by LCM of 2 & 3 = 6

Now the numbers between 170 and 320 which are divisible by 6 are

174 , 180 , 186 , ...., 318

This is an arithmetic progression

First term = a = 174

Common Difference = d = 6

Let 318 be the nth term

So by the given condition

$\sf{174 + (n - 1) \times 6 = 318}$

$\sf{ \implies \: (n - 1) \times 6 = 144}$

$\sf{ \implies \: (n - 1) = 24}$

$\sf{ \implies \: n = 25}$

Hence the numbers between 170 and 320 which are divisible by both 2 and 3 is 25

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Answer 2

Answer:

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