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14 votes
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The exponent of $11$ in the prime factorization of $300!$ is

  1. $27$
  2. $28$
  3. $29$
  4. $30$
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3 Answers

Best answer
86 votes
86 votes
Simple Method:

$\lfloor 300/11\rfloor =27$

$\lfloor 27/11\rfloor =2$

$\lfloor 2/11\rfloor =0$

Repeat this and when get $0$ stop and sum all the results.

Ans: $27 + 2 +0=29.$

Correct Answer: $C$
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56 votes
56 votes
300! is 1*2*3*...*300

Now there are 27 multiples of 11 from 1 to 300, so they will include 11 as a prime factor atleast once.

121 and 242 will contain an extra 11, all other will contain 11 as a factor only once.

So, total number of 11's = 27+2 = 29.

So, exponent of 11 is 29 i.e. option C.
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11 votes
11 votes

Here answer is 29.

Divide 300/11=> you get that there are 27 Multiple of 11.

Then there are two numbers

121, 242

121 = 112

242 = 112 * 2

Because of this two number we get exponent as => 27 + 2 = 29. (One extra for each no !)

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Answer:

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