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.

assuolareuz

assuolareuz

Answered question

2022-08-05

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.

Answer & Explanation

burgesia1w

burgesia1w

Beginner2022-08-06Added 11 answers

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

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