The total number of 3 -digit numbers, whose greatest common divisor with 36 is 2 , is ______.

Step-by-step solution

Prime factorisation of 36 = 2 × 2 × 3 × 3 So, for number having G.C.D with 36 to be 2 , the number should be odd multiple of 2 and does not have factor 3 and 9 ⇒ Odd multiple of 2 are 102 , 106 , 110 , 114 … … . 998     225   numbers ⇒ No. of multiples of 3 are 102 , 114 , 126 … … . 990   75   numbers Which also include multiple of 9 Hence, Required = 225 - 75 = 150