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If a = 16b and b is a prime number greater than 2, how many positive

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Math Expert
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Joined: 02 Sep 2009
Posts: 52161
If a = 16b and b is a prime number greater than 2, how many positive  [#permalink]

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New post 17 Dec 2018, 01:46
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

64% (00:49) correct 36% (00:58) wrong based on 63 sessions

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Director
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Concentration: Accounting, Finance
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Re: If a = 16b and b is a prime number greater than 2, how many positive  [#permalink]

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New post 17 Dec 2018, 02:21
Bunuel wrote:
If a = 16b and b is a prime number greater than 2, how many positive distinct factors does a have?

A. 4
B. 5
C. 6
D. 8
E. 10


b = 3.

a = 16b

a = 16*3 = 48.

1 * 48 = 48
2*24=48
3*16=48
4*12=48
6*8=48.

we have 10 factors.

E is the correct answer.
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Re: If a = 16b and b is a prime number greater than 2, how many positive  [#permalink]

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New post 17 Dec 2018, 05:57
1
\(a = 16(prime)\)

\(a = 2^4(prime)^1\)

A prime number can only take 1 as its power. Apart from that if takes any other power, then b will not be a prime number.

So a has (4+1)(1+1) = 5*2 = 10 factors.

OPTION: E
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Re: If a = 16b and b is a prime number greater than 2, how many positive  [#permalink]

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New post 17 Dec 2018, 08:57
Bunuel wrote:
Finding the Number of Factors of an Integer

First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.

The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)

Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.



a = 2^4 * b^1 where b is a prime <> 2

Number of factors is (4+1)(1+1) = 10.

Answer E
GMAT Club Bot
Re: If a = 16b and b is a prime number greater than 2, how many positive &nbs [#permalink] 17 Dec 2018, 08:57
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