Question

how many 3 digit numbers are divisible by 7

Answer 1

numbers begin from 105 .......994

here a= 105
l= 994
n=?
d= 7
so
994 = 105+(n-1) 7
= 105+7n-7
994= 98+7n
994-98 = 7n
896/7 = n
n= 128
so 128 three digit numbers are divisible by 7
I guess......

Answer 2

Given,

The numbers are of 3 digits

To find,

The number of digit numbers which are divisible by 7

Solution,

We can easily solve this mathematical problem by using the following mathematical process.

Now, by mental calculations, we need to know following two things

1. The first ever 3 digit number which is divisible by 7 = 105
2. The last 3 digit number which is divisible by 7 = 994

Now, with the help of the Arithmetic progression formula, we can easily calculate the total number of digits.

First term of AP (a) = 105

Common difference (d) = 7 (because they are divisible by 7, so two consecutive numbers will have difference of their divisor.)

Last term = 994

Total terms = Let, n

According to the data mentioned in the question,

994 = 105 + (n-1)×7

994 = 105 + 7n - 7

994 = 98 + 7n

7n = 896

n = 128

Hence, there will be 128 digits.