The total number of -digit numbers whose greatest common divisor with is , is
Find the total number of -digit numbers:
Let be the four digit number.
Gcd
Thus is an odd integer which is divisible by but not by .
Since -digit odd multiplies of are,
We can see that it is an A.P. with
Since, term of A.P. is given by
Now, digit odd multiplies of are,
It is an A.P. with
Since, term of A.P. is given by
Therefore, total such numbers
Hence, total number of -digit numbers whose greatest common divisor with is , is .