JEE MAIN - Mathematics (2023 - 29th January Evening Shift - No. 16)
The total number of 4-digit numbers whose greatest common divisor with 54 is 2, is __________.
Answer
3000
Explanation
$$\gcd (a,54) = 2$$ 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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