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Which of the following values has the greatest number of unique factor

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Which of the following values has the greatest number of unique factor  [#permalink]

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New post 22 May 2018, 04:26
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

81% (00:37) correct 19% (00:41) wrong based on 47 sessions

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Which of the following values has the greatest number of unique factor  [#permalink]

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New post 22 May 2018, 05:10
Bunuel wrote:
Which of the following values has the greatest number of unique factors?

A. 30
B. 31
C. 32
D. 33
E. 34



30. Factors are 1,2,3,5,6,10,15,30 = 8 unique factors
31. Factors are 1, 31 = 2 unique factors
32. Factors are 1,2,4,8,16,32 = 6 unique factors
33. Factors are 1,3,11,33 = 4 unique factors
34. Factors are 1,2,17,34 = 4 unique factors


Hence option A = 30 is the answer.
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Re: Which of the following values has the greatest number of unique factor  [#permalink]

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New post 22 May 2018, 05:23

Solution



To find:
• From the numbers given in the options, which number has the greatest number of unique factors

Approach and Working:
We can express each of the numbers in terms of its prime factors and then figure out the number of factors for each of them
• 30 = \(2^1 * 3^1 * 5^1\)
    o Number of factors = (1 + 1) * (1 + 1) * (1 + 1) = 8
• 31 = \(31^1\)
    o Number of factors = 1 + 1 = 2
• 32 = \(2^5\)
    o Number of factors = 5 + 1 = 6
• 33 = \(3^1 * 11^1\)
    o Number of factors = (1 + 1) * (1 + 1) = 4
• 34 = \(2^1 * 17^1\)
    o Number of factors = (1 + 1) * (1 + 1) = 4

We can see the number 30 has greatest number of factors
Hence, the correct answer is option A.

Answer: A
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Re: Which of the following values has the greatest number of unique factor &nbs [#permalink] 22 May 2018, 05:23
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