Question

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

Answer 1

Answer is 1000

Let N be the four digit number

gcd(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

4 digit odd multiples of 9

1017, 1035,......., 9999 → 500

Hence number of such N = 1000

Answer 2

Let N be the four digit number gcd(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 4 digit odd multiples of 9 1017, 1035,......., 9999 → 500

N=1000

Answer 3

Let N be the four digit number GCD (N,18) = 3 Hence N is an odd integer which is divisible by 3 but not by 9.

 4 digit odd multiples of 3 are 1005, 1011,......., 9999 → 1500

 4 digit odd multiples of 9 are 1017, 1035,......., 9999 → 500

 Hence number of such N = 1000