Question

Question 13
How many three-digit numbers are divisible by 7?

Answer 1

First, three-digit number that is divisible by 7 is 105.
Next number = 105 + 7 = 112
Therefore, required numbers are 105, 112, 119……
All are three-digit numbers which are divisible by 7 and thus, all these are terms of an A.P. having the first term as 105 and common difference as 7.
The maximum possible three-digit number is 999. When we divide it by 7, the remainder will be 5. Clearly, 999 – 5 = 994 is the maximum possible three-digit number that is divisible by 7.
The series is as follows
105, 112, 119, …., 994
Let 994 be the nth term of this A.P.
$a=105d=7a_n=994n=?a_n=a+(n-1)d994=105+(n-1)7889=(n-1)7(n-1)=127$
Therefore, 128 three-digit numbers are divisible by 7.