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The integer K is positive, but less than 400. If 21K is a multiple of

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The integer K is positive, but less than 400. If 21K is a multiple of [#permalink] New post   23 May 2021, 23:50
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The integer K is positive, but less than 400. If 21K is a multiple of 180, how many unique prime factors does K have?

A. 1

B. 2

C. 3

D. 4

E. 5
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C
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Re: The integer K is positive, but less than 400. If 21K is a multiple of [#permalink] New post   24 May 2021, 00:37
c.
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Re: The integer K is positive, but less than 400. If 21K is a multiple of [#permalink] New post   24 May 2021, 07:48
is it option d?
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Re: The integer K is positive, but less than 400. If 21K is a multiple of [#permalink] New post   24 May 2021, 08:03
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21K is a multiple of 180

\(3 * 7 * K = 3 * 3 * 4 * 5 * x\)

\(7 * K = 60 * x\)

Hence \(K\) will be \(60\) and \(x\) will be \(7\)

Factors of \(60 = 1 , 2 , 3 , 4 , 5 , 6 , 10 , 12 , 15 , 20 , 30 , 60\)

Unique prime factors = \(2 , 3 , 5\)

Answer C
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Re: The integer K is positive, but less than 400. If 21K is a multiple of [#permalink] New post   28 Apr 2023, 11:27
↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧




Given that The integer K is positive, but less than 400 and 21K is a multiple of 180. And we need to find how many unique prime factors does K have?

21K is a multiple of 180
=> 21K is divisible by 180
21K = 3*7*K and 180 = 3*60

So, for 21K to be divisible by 60
K should be divisible by 60

=> K is a multiple of 60 (=2^2 * 3 * 5)
Unique prime factors of K = 3

So, Answer will be C
Hope it helps!

Watch the following video to learn the basics of Factors and Multiples

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gmatclubot
Re: The integer K is positive, but less than 400. If 21K is a multiple of [#permalink]
28 Apr 2023, 11:27
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