Let ( 111...1 ) ( n t i m e s ) , then(a) a 912 is not prime.(b) a 951 is not prime.c) a 480 is not prime.d) a 91 is not prime.

Question

Let   (  111...1      )          (      n             t      i      m      e      s      )      , then(a)       a          912       is not prime.(b)       a          951       is not prime.c)       a          480       is not prime.d)       a          91       is not prime.

burgesia1w · Accepted Answer

Step 1For prime numbers, their are only two factors.1 and 2 itselfBut here a)       a          912        =  (  111...1      )          912      t      i      m      e      s      And from divisibility rules of 3if the sum of digits is divisible by 3 then the number is divisible by 3Here   1  +  1  +  1  −  −  −  −      11          912      t      i      m      e      s        =  912And       912    3    ⇒  304 (so its sum divisible by 3)So       a          912       has a factor 3.So this is a prime numberStep 2b)       a          951        ⇒      951    3    =  317 (sum divisible)so its a prime numberc)       a          480        ⇒      480    3    ⇒  160  ⇒ prime numberd)       a          91        ⇒      91    3    ⇒  30.333 (sum is not divisible by 3)so its not primeanswer: (D)       a          91       is not prime

Let a_n= ubrace(111...1)_("n times"), then a)a_{912} is not prime b) a_{951} is not prime c) a_{480} is not prime d) a_{91} is not prime.

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