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# How many three-digit numbers are divisible by 7?

**Solution:**

We have to find the number of three-digit numbers which are divisible by 7.

aₙ = a + (n - 1)d is the n^{th} term of AP.

Here, aₙ_{ }is the n^{th} term, a is the first term, d is the common difference and n is the number of terms.

First three-digit number that is divisible by 7 = 105

Next number = 105 + 7 = 112

Therefore, the series becomes 105, 112, 119, ...

Thus, 105, 112, 119, ... is forming an A.P. having the first term as 105 and a common difference of 7.

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

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

Hence the final sequence is as follows:

105, 112, 119, ..., 994

Let 994 be the n^{th} term of this A.P.

a = 105

d = 7

aₙ = 994

n = ?

We know that the n^{th} term of an A.P. is, aₙ = a + (n - 1)d

994 = 105 + (n - 1)7

889 = (n - 1)7

n - 1 = 889/7

n - 1 = 127

n = 127 + 1

n = 128

There are 128 three-digit numbers that are divisible by 7

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 5

**Video Solution:**

## How many three-digit numbers are divisible by 7?

NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2 Question 13

**Summary:**

The number of three-digit numbers divisible by 7 is 128.

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