The total number of 4-digit numbers whose greatest common divisor with 54 is 2, is __________.
Answer (integer)
3000
Solution
<p>$\gcd (a,54) = 2$ when a is a 4 digit no.</p>
<p>And $54 = 3 \times 3 \times 3 \times 2$</p>
<p>So, $a=$ all even no. of 4 digits $-$ Even multiple of 3 (4 digits)</p>
<p>$= 4500 - 1500$</p>
<p>$= 3000$</p>
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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