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# How many unique factors does 96 have?

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Math Expert
Joined: 02 Sep 2009
Posts: 58465
How many unique factors does 96 have?  [#permalink]

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08 Jul 2017, 05:38
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5% (low)

Question Stats:

84% (00:49) correct 16% (01:15) wrong based on 159 sessions

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How many unique factors does 96 have?

A. 8
B. 10
C. 12
D. 14
E. 15

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Joined: 23 May 2017
Posts: 234
Concentration: Finance, Accounting
WE: Programming (Energy and Utilities)
Re: How many unique factors does 96 have?  [#permalink]

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08 Jul 2017, 05:41
prime factors of 96 = 2^5 * 3 = number of factors = 6 * 2 = 12

Ans= C
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Re: How many unique factors does 96 have?  [#permalink]

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08 Jul 2017, 05:53
1
1
Bunuel wrote:
How many unique factors does 96 have?

A. 8
B. 10
C. 12
D. 14
E. 15

$$n = a^p*b^q$$ -------------- ($$a$$ and $$b$$ are prime factors of $$n$$ and $$p$$ and $$q$$ are their powers)

Number of factors of $$n$$ will be expressed by formula $$(p+1)(q+1)$$

Prime factors of $$96 = 2^5 * 3^1$$

Number of unique factors $$= (5+1)(1+1) = 6*2 = 12$$

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How many unique factors does 96 have?  [#permalink]

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08 Jul 2017, 07:32
Bunuel wrote:
How many unique factors does 96 have?

A. 8
B. 10
C. 12
D. 14
E. 15

For me, learning the method was a lot easier than remembering the formula (kudos to sashiim20 ), so

1. Find prime factors of 96 =>
2*2*2*2*2*3, or $$2^53^1$$

2. Take the power of each prime factor and add 1

5+1 = 6 and
1+1= 2

3. Multiply results: 6*2 = 12, which includes all of the distinct factors of 96 including 96 and 1.

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Re: How many unique factors does 96 have?  [#permalink]

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08 Jul 2017, 07:42
Top Contributor
Bunuel wrote:
How many unique factors does 96 have?

A. 8
B. 10
C. 12
D. 14
E. 15

The posters above have used a useful rule (which I am providing a video for below). However, if you weren't aware of that rule, you can always just list the factors.

When doing so, find pairs, starting from the lowest and biggest factors. We get:

Factors of 96: {1, 96}
Factors of 96: {1, 2, 48, 96}
Factors of 96: {1, 2, 3, 32, 48, 96}
.
.
.
and so on..
.
Factors of 96: {1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96}
12 factors

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Re: How many unique factors does 96 have?   [#permalink] 08 Jul 2017, 07:42
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