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# How many three digit numbers are divisible by 7? Q.13

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In NCERT how to solve the question of arithmetic progressions of exercise 5.2 of class 10th of math. How to solve this problem How many three digit numbers are divisible by 7?

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1. First three-digit number that is divisible by 7 are;

First number = 105

Second number = 105+7 = 112

Third number = 112+7 =119

Therefore, 105, 112, 119, â€¦

All are three digit numbers are divisible by 7 and thus, all these are terms of an A.P. having first term as 105 and common difference as 7.

As we know, the largest possible three-digit number is 999.

When we divide 999 by 7, the remainder will be 5.

Therefore, 999-5 = 994 is the maximum possible three-digit number that is divisible by 7.

Now the series is as follows.

105, 112, 119, â€¦, 994

Let 994 be theÂ nth term of this A.P.

first term, aÂ = 105

common difference, dÂ = 7

anÂ = 994

nÂ = ?

As we know,

anÂ =Â a+(nâˆ’1)d

994 = 105+(nâˆ’1)7

889 = (nâˆ’1)7

(nâˆ’1) = 127

nÂ = 128

Therefore, 128 three-digit numbers are divisible by 7.

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