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The number of distinct factors of 32

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The number of distinct factors of 32 [#permalink] New post 30 Aug 2018, 16:39
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Question Stats:

59% (00:43) correct 40% (00:24) wrong based on 61 sessions
Quantity A
Quantity B
The number of distinct positive factors of 32
The number of distinct positive factors of 20


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Sandy
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Re: The number of distinct factors of 32 [#permalink] New post 01 Sep 2018, 10:07
sandy wrote:
Quantity A
Quantity B
The number of distinct positive factors of 32
The number of distinct positive factors of 20


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


Rule : First make prime factorization of an integer N = a^p * b ^q * c^r , where a, b , and c and are prime factors of and p , q , and r are their powers.
The number of factors of will be expressed by the formula (p+1) (q+1) (r+1). NOTE: this will include 1 and n itself.


Now factorise Col A : we get 2^5 and
Col B : 2^2 * 5^1.

As per above formula Col A : (5+1) = 6
Col B : (2+1)(1+1) = 6.

Both same .

C.
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Re: The number of distinct factors of 32 [#permalink] New post 07 Jul 2019, 05:14
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Expert's post
sandy wrote:
Quantity A
Quantity B
The number of distinct positive factors of 32
The number of distinct positive factors of 20


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


Alternatively, we can just list and count the positive factors of 32 and 20

QUANTITY A: Factors of 32: 1, 2, 4, 8, 16, 32 (6 factors)
QUANTITY B: Factors of 20: 1, 2, 4, 5, 10, 20 (6 factors)

Answer: C

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
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Re: The number of distinct factors of 32 [#permalink] New post 21 Jun 2020, 07:13
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A
1*32
2*16
4*8
Seems we have 6 factors

B
1*20
2*10
4*5
Again, we have 6 factors here as well

C is the right answer
Re: The number of distinct factors of 32   [#permalink] 21 Jun 2020, 07:13
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