QJEEM23Ma49a5: JEE Main 2023 Mathematics - Class 11 JEEM23Ma49a5 Solution: The total number of 4-digit numbers whose greatest common…

Question

Verified Solution • 2025–26 Session moderate

The total number of 4-digit numbers whose greatest common divisor with 54 is 2, is __________.

Accepted Answer

$gcd (a, 54) = 2$ when a is a 4 digit no.

And $54 = 3 \times 3 \times 3 \times 2$

So, $a =$ all even no. of 4 digits $-$ Even multiple of 3 (4 digits)

$= 4500 - 1500$

$= 3000$

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