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

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Math Expert
Joined: 02 Sep 2009
Posts: 54369
How many distinct factors do 165 and 300 have in common?  [#permalink]

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01 Jul 2017, 00:15
1
00:00

Difficulty:

55% (hard)

Question Stats:

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

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

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

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

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01 Jul 2017, 00:30
1
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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01 Jul 2017, 01:20
1
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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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 $$300$$ $$= (1+1)(1+1) = 2*2 = 4$$

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