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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
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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17 Dec 2018, 01:46
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Difficulty:

45% (medium)

Question Stats:

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

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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

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Director
Joined: 31 Oct 2013
Posts: 951
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If a = 16b and b is a prime number greater than 2, how many positive  [#permalink]

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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.

Manager
Joined: 13 Jan 2018
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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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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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Joined: 05 Oct 2018
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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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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.

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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