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How many distinct factors do 165 and 300 have in common?

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How many distinct factors do 165 and 300 have in common?  [#permalink]

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New post 01 Jul 2017, 00:15
1
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

47% (01:24) correct 53% (01:20) wrong based on 95 sessions

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Re: How many distinct factors do 165 and 300 have in common?  [#permalink]

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New post 01 Jul 2017, 00:30
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Bunuel wrote:
How many distinct factors do 165 and 300 have in common?

A. 2
B. 3
C. 4
D. 5
E. 8


Factors of 165 (5*3*11) = 1,3,5,11,15,33,55,165

Factors of 300 (2*2*3*5*5) = 1,2,3,4,5,6,10,12,15,20,25,30,60,75,100,150,200,300

Distinct common Factors = 1,3,5,15

C
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Re: How many distinct factors do 165 and 300 have in common?  [#permalink]

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New post 01 Jul 2017, 01:20
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1
When prime-factorized, \(165 = 3*5*11\) and \(300 = 2^3 * 3 * 5^2\)

The common factors of the numbers 165 and 300 are 3 and 5.
Since we have been asked to find the distinct common factors,
they will be 1,3,5 and 3*5(15) which is 4(Option C)
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Re: How many distinct factors do 165 and 300 have in common?  [#permalink]

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New post 01 Jul 2017, 01:41
2
Bunuel wrote:
How many distinct factors do 165 and 300 have in common?

A. 2
B. 3
C. 4
D. 5
E. 8


By Prime factorization of \(165\) and \(300\), we get;

\(165 = 3 * 5 * 11\)

\(300 = 2^2 * 3 * 5^2\)

Common factors between \(165\) and \(300\) is one \(3\) and one \(5\) \(= 3^1*5^1\)

Number of factors is expressed by the formula \(= (p+1)(q+1)\) ------------- (where \(p\) and \(q\) are powers of the prime factors.)

Number of common factors between \(165\) and \(300\) \(= (1+1)(1+1) = 2*2 = 4\)

Answer (C)...
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Re: How many distinct factors do 165 and 300 have in common?   [#permalink] 01 Jul 2017, 01:41
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