How many three digit natural numbers are divisible by 7?

Given: Three digit natural numbers.

To do: To find how many Three digit natural numbers are divisible by $7=?$

We know that all three digit natural numbers are 100 to 999.

And first three digit number divisible by $7=105$

And if we divide 999 by 7 remainder will be 5.

After subtracting 5 from 999, we have 994.

$\therefore$  994 is the last three digit natural number divisible by 7.

Therefor the series is $105,\ 112,\ 119,\dotsc \dotsc \dotsc \dotsc ..\ 994$

It is an A.P.

Here first term $a=105$, last term $l=994$, common difference $d=7$

Number of terms $n=?$

And we know that $n^{th}\ term\ a_{n}=a+( n-1) d$

$\therefore 994=105+( n-1) \times 7$

$\Rightarrow ( n-1) \times 7=994-105=889$

$\Rightarrow n-1=\frac{889}{7} =127$

$\Rightarrow n=127+1=128$

$\therefore$ There are 128 three digit natural numbers which are divisible by 7.