The sum of all the elements of the set $\{ \alpha \in \{ 1,2,.....,100\} :HCF(\alpha ,24) = 1\}$ is __________.
Answer (integer)
1633
Solution
<p>The numbers upto 24 which gives g.c.d. with 24 equals to 1 are 1, 5, 7, 11, 13, 17, 19 and 23.</p>
<p>Sum of these numbers = 96</p>
<p>There are four such blocks and a number 97 is there upto 100.</p>
<p>$\therefore$ Complete sum</p>
<p>= 96 + (24 $\times$ 8 + 96) + (48 $\times$ 8 + 96) + (72 $\times$ 8 + 96) + 97</p>
<p>= 1633</p>
About this question
Subject: Mathematics · Chapter: Sets, Relations and Functions · Topic: Sets and Operations
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