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Number of prime factors of 20!/10!
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05 Jul 2023, 04:46
05 Jul 2023, 04:46
2
Expert Reply
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Question Stats:
37% (01:20) correct
62% (01:03) wrong based on 98 sessions
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Quantity A |
Quantity B |
Number of prime factors of \(\frac{20!}{10!}\) |
Number of prime factors of \(\frac{20!}{5!}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Number of prime factors of 20!/10!
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25 Jul 2023, 10:13
25 Jul 2023, 10:13
1
Expert Reply
\(\frac{20!}{10!}\) is
\(\frac{20*19*18.......*11*10!}{10!}=20*19*18.....*11\)
20!/5! is
\(\frac{20*19*18.........*6*5!}{5!}=20*19*18...........*7*6\)
Now, whatever prime factors we have in Quantity A will be present in Quantity B as well. The only difference will be created by the extra numbers 10 × 9 × 8 × 7 × 6 in Quantity B.
But since we need to consider only prime factors hence, the prime factors of 10 will be 2 and 5 which is present in 20 as well.
Similarly, the prime factor of 9 which is 3 is present in 18 as well.
The prime factor of 8 which is 2 is present in 16, the prime factor of 7 is present in 14 and the prime factors of 6 which is 2 and 3 is present in 12 as well.
Thus, Quantity A and Quantity B will have same number of prime factors.
Ans. (C)
\(\frac{20*19*18.......*11*10!}{10!}=20*19*18.....*11\)
20!/5! is
\(\frac{20*19*18.........*6*5!}{5!}=20*19*18...........*7*6\)
Now, whatever prime factors we have in Quantity A will be present in Quantity B as well. The only difference will be created by the extra numbers 10 × 9 × 8 × 7 × 6 in Quantity B.
But since we need to consider only prime factors hence, the prime factors of 10 will be 2 and 5 which is present in 20 as well.
Similarly, the prime factor of 9 which is 3 is present in 18 as well.
The prime factor of 8 which is 2 is present in 16, the prime factor of 7 is present in 14 and the prime factors of 6 which is 2 and 3 is present in 12 as well.
Thus, Quantity A and Quantity B will have same number of prime factors.
Ans. (C)
Re: Number of prime factors of 20!/10!
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13 Jan 2024, 15:37
13 Jan 2024, 15:37
2
But the question is not asking about unique prime factor rather it is asking about the number of prime factors. So I think answer should be B.
