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If 2^5, 3^3, and 13^2 are all factors of the product of 936 and w wher

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Bunuel
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If 2^5, 3^3, and 13^2 are all factors of the product of 936 and w wher [#permalink] New post   25 Apr 2016, 03:54
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If 2^5, 3^3, and 13^2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w?

A. 26
B. 39
C. 42
D. 65
E. 156
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E
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stonecold
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Re: If 2^5, 3^3, and 13^2 are all factors of the product of 936 and w wher [#permalink] New post   25 Apr 2016, 06:11
Here 156 has three two's
two three's
and one 13
rest of them must be in w
so w= 13*3*4 = 156

Smash E
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PhilSad92
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Re: If 2^5, 3^3, and 13^2 are all factors of the product of 936 and w wher [#permalink] New post   28 Apr 2016, 05:01
stonecold wrote:
Here 156 has three two's
two three's
and one 13
rest of them must be in w
so w= 13*3*4 = 156

Smash E


E) is the right answer, but don't you mean 936 in the first sentence?

936= 2^3 *3^2 *13^1

So what you need is 2 more 2's, 1 more 3 and 1 more 13.
This gives us 2^2 *3 *13=156 E)
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Re: If 2^5, 3^3, and 13^2 are all factors of the product of 936 and w wher [#permalink] New post   28 Apr 2016, 11:33
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PhilSad92 wrote:
stonecold wrote:
Here 156 has three two's
two three's
and one 13
rest of them must be in w
so w= 13*3*4 = 156

Smash E


E) is the right answer, but don't you mean 936 in the first sentence?

936= 2^3 *3^2 *13^1

So what you need is 2 more 2's, 1 more 3 and 1 more 13.
This gives us 2^2 *3 *13=156 E)


Yup definitely its a TYPO

\(936\)= \(2^3\)x \(3^2\)x \(13^1\)
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riyan
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Re: If 2^5, 3^3, and 13^2 are all factors of the product of 936 and w wher [#permalink] New post   12 Dec 2017, 12:28
2^5, 3^3, and 13^2 are all factors of the product of 936 and w
936=2^33^213
So, we left with 2^2*3*13=156
Hence answer is E
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MathRevolution
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Re: If 2^5, 3^3, and 13^2 are all factors of the product of 936 and w wher [#permalink] New post   02 Oct 2020, 01:40
Expert Reply
936 = \(2^3 * 3^2\) * 13

Factors are: \(2^5, 3^3, 13^2 \)

Therefore 936 * w = \(2^5 * 3^3 * 13^2 \)

=> \(2^3 * 3^2\) * 13 * w = \(2^5 * 3^3 * 13^2 \)

=> w = \(2^2\) * 3 * 13 = 156

Answer E
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Re: If 2^5, 3^3, and 13^2 are all factors of the product of 936 and w wher [#permalink]
02 Oct 2020, 01:40
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