The total number of 4 -digit numbers whose greatest common divisor with 18 is 3 is _____.

Step-by-step solution

Let N be the four digit number g c d N , 18 = 3 Hence N is an odd integer which is divisible by 3 but not by 9 . 4 digit odd multiples of 3 1005 , 1011 , … , 9999 → 1500 digit odd multiples of 9 1017 , 1035 , … , 9999 → 500 Hence number of such N = 1500 - 500 = 1000