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What is the quotient of 5040 divided by the product of its unique

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Ravixxx
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What is the quotient of 5040 divided by the product of its unique [#permalink] New post   Updated on: 05 May 2020, 22:02
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What is the quotient of 5040 divided by the product of its unique prime factors?

(A) 18
(B) 20
(C) 22
(D) 24
(E) 26
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D

Originally posted by Ravixxx on 21 Apr 2020, 10:11.
Last edited by Ravixxx on 05 May 2020, 22:02, edited 1 time in total.
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Re: What is the quotient of 5040 divided by the product of its unique [#permalink] New post   21 Apr 2020, 10:13
Solution:

\(5040 = 2^{4}* 3^{2}*5*7\)

Product of prime factor = \(2*3*5*7 = 210\)

\(\frac{5040}{210} = 24\)

Answer D
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Re: What is the quotient of 5040 divided by the product of its unique [#permalink] New post   28 Apr 2020, 06:17
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It’s easy to recognize that 5040 is 7!. This helps us realise that there are exactly 4 unique prime factors (disregarding the powers) for 5040 i.e. 2,3 5 and 7.

The product of these prime factors = 2 X 3 X 5 X 7 = 210.
When 5040 is divided by 210, the quotient is 24 since 210 X 24 = 5040.

The correct answer option is D.

Hope that helps!
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Re: What is the quotient of 5040 divided by the product of its unique [#permalink] New post   05 May 2020, 17:28
This question is misleading.

It should say "prime factors" not "prime factor".
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Re: What is the quotient of 5040 divided by the product of its unique [#permalink] New post   05 May 2020, 22:03
Tumilara wrote:
This question is misleading.

It should say "prime factors" not "prime factor".


Thank you, I edit the question.

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Re: What is the quotient of 5040 divided by the product of its unique [#permalink] New post   16 May 2020, 07:24
ArvindCrackVerbal wrote:
It’s easy to recognize that 5040 is 7!. This helps us realise that there are exactly 4 unique prime factors (disregarding the powers) for 5040 i.e. 2,3 5 and 7.



The product of these prime factors = 2 X 3 X 5 X 7 = 210.
When 5040 is divided by 210, the quotient is 24 since 210 X 24 = 5040.

How did you recognize that 5040 is 7! and there are exactly 4 unique prime factors?

The correct answer option is D.

Hope that helps!
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Re: What is the quotient of 5040 divided by the product of its unique [#permalink] New post   16 May 2020, 14:45
Ravixxx wrote:
What is the quotient of 5040 divided by the product of its unique prime factors?

(A) 18
(B) 20
(C) 22
(D) 24
(E) 26


5040 = 2^4 x 3^2 x 5 x 7 (say this is A)
Product of prime factors = 2 x 3 x 5 x 7 (say this is B)
Hence, the quotient = A/B = 2^3 x 3 = 24 (option D)

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Re: What is the quotient of 5040 divided by the product of its unique [#permalink]
16 May 2020, 14:45
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