The total number of 3-digit numbers, whose greatest common divisor with 36 is 2, is ___________.
Answer (integer)
150
Solution
<p>$\because$ x $\in$ [100, 999], x $\in$ N</p>
<p>Then ${x \over 2}$ $\in$ [50, 499], ${x \over 2}$ $\in$ N</p>
<p>Number whose G.C.D. with 18 is 1 in this range have the required condition. There are 6 such number from 18 $\times$ 3 to 18 $\times$ 4. Similarly from 18 $\times$ 4 to 18 $\times$ 5 ......., 26 $\times$ 18 to 27 $\times$ 18</p>
<p>$\therefore$ Total numbers = 24 $\times$ 6 + 6 = 150</p>
<p>The extra numbers are 53, 487, 491, 493, 497 and 499.</p>
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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