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QJEEM21Ma7ff0: JEE Main 2021 Mathematics - Class 11 JEEM21Ma7ff0 Solution: The total number of 4-digit numbers whose greatest common…

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

Step-by-Step Verified Solution

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 →\to 1500

4 digit odd multiples of 9

1017, 1035, ..........., 9999 →\to 500

Hence number of such N = 1000

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