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Which of the following is NOT a factor of the product of the

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Which of the following is NOT a factor of the product of the  [#permalink]

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14 Aug 2013, 20:06
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Which of the following is NOT a factor of the product of the first 50 positive multiples of 4 ?

A. $$17^2$$
B. $$11^4$$
C. $$7^6$$
D. $$47^{12}$$
E. $$2^{124}$$

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Which of the following is NOT a factor of the product of the  [#permalink]

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14 Aug 2013, 20:18
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gmatpapa wrote:
Which of the following is NOT a factor of the product of the first 50 positive multiples of 4 ?

A. $$17^2$$
B. $$11^4$$
C. $$7^6$$
D. $$47^{12}$$
E. $$2^{124}$$

product of the first 50 positive multiples of 4 = 4*8*12*16*......200 =4^50*(1*2*3......49*50) = 2^100(FACTORIAL 50)

lets check options:

A. $$17^2$$ ==>we need two 17 ==>that can be found in FACTORIAL 50 (17,34)=>factor

B. $$11^4$$ ==>we need four 11==> that can be found in FACTORIAL 50 (11,22,33,44)=>factor

C. $$7^6$$ ==>we need six 7 ==>that can be found in FACTORIAL 50(7,14,21,28,35,42)=>factor

D. $$47^{12}$$==>not a factor since we 47 is a prime and is only 1 time present in factorial 50

E. $$2^{124}$$==>This can be found as we have 2 ^100 and in factorial 50 we have 25 even numbers=>factor

hence D
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Re: Which of the following is NOT a factor of the product of the  [#permalink]

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15 Aug 2013, 05:08
gmatpapa wrote:
Which of the following is NOT a factor of the product of the first 50 positive multiples of 4 ?

A. $$17^2$$
B. $$11^4$$
C. $$7^6$$
D. $$47^{12}$$
E. $$2^{124}$$

4^50×(1.2.3.4.5.6.7..............................50)

= 4^50 (1.2.3.4.................50)

17^2 = 17 ×17 (we have 17 and 34) so this is a factor.

11× 11× 11× 11 (we have 11,22,33,44) so this is a factor.

7 × 7× 7× 7 ×7 ×7 (we have 7,14,21,28,35,42) so this is a factor.

2^124 = (4)^62 . Now 4^50 / 4^62 = 1/4^12 = 1/(4 . 4 . 4. 4. 4. 4. 4. 4. 4. 4. 4. 4) we have (4,8,12,16,20,24,28,32,36,40,44,48) . so this is also a factor.

These left only one as the guilty and it's 47^12
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Re: Which of the following is NOT a factor of the product of the  [#permalink]

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15 Jan 2017, 08:14
Firstly the product of first positive 50 multiples of 4=>
4*1*4*2*4*3*4*4*4*5.....4*50=> 4^50*50!
Secondly notice Option D is 47^2 and 47 is a prime number.
Number of 47's in 4^50*50!=> one
Hence 47^2 will never be its factor.

Hence D.

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Re: Which of the following is NOT a factor of the product of the  [#permalink]

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28 Mar 2017, 08:32
Hi Bunuel
Can you please give your explanation for this question..All the 50 multiples of 4 would be even, then how come 17 is a factor of this product?
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Re: Which of the following is NOT a factor of the product of the  [#permalink]

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28 Mar 2017, 10:10
Shiv2016 wrote:
Hi Bunuel
Can you please give your explanation for this question..All the 50 multiples of 4 would be even, then how come 17 is a factor of this product?

My solution would be the same as this one: https://gmatclub.com/forum/which-of-the ... l#p1257006
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Re: Which of the following is NOT a factor of the product of the  [#permalink]

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28 Mar 2017, 10:32
Shiv2016 wrote:
Hi Bunuel
Can you please give your explanation for this question..All the 50 multiples of 4 would be even, then how come 17 is a factor of this product?

Also, are you saying that even number cannot have an odd factor? It's not true. For example, 4*17 = 68 is even and is a multiple of 17.
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Re: Which of the following is NOT a factor of the product of the  [#permalink]

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06 Feb 2019, 18:39
gmatpapa wrote:
Which of the following is NOT a factor of the product of the first 50 positive multiples of 4 ?

A. $$17^2$$
B. $$11^4$$
C. $$7^6$$
D. $$47^{12}$$
E. $$2^{124}$$

Since the first positive multiple of 4 is 4 and the 50th is 200, we see that in the product of the numbers of:

4 x 8 x 12 x 16…..x 196 x 200, we won’t have 12 factors of 47, and thus, 47^12 is not a factor of the first 50 multiples of 4. (Note: 47 is prime, and in the product 4 x 8 x 12 x 16…..x 196 x 200, there is only one factor of 47, which is in 188.)

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Re: Which of the following is NOT a factor of the product of the  [#permalink]

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06 May 2020, 00:41
Hi,

Can some please explain how can the below quoted portion

Quote:
product of the first 50 positive multiples of 4 = 4*8*12*16*......200

Equal to

Quote:
4^50*(1*2*3......49*50) = 2^100(FACTORIAL 50)

Without skipping any simplification steps?

Re: Which of the following is NOT a factor of the product of the   [#permalink] 06 May 2020, 00:41