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What is the product of all positive factors of 18?

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What is the product of all positive factors of 18?  [#permalink]

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New post 10 Mar 2016, 05:03
1
4
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

74% (01:09) correct 26% (01:01) wrong based on 173 sessions

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Re: What is the product of all positive factors of 18?  [#permalink]

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New post 10 Mar 2016, 05:12
Positive factors of 18 are 1,2,3,6,9, and 18. The factors set up 3 pairs of 18 (18*1, 2*9, 3*6), hence its product is 18^3, which is 5832. I would go for E, then.
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Re: What is the product of all positive factors of 18?  [#permalink]

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New post 10 Mar 2016, 05:56
Prime Factorization of 18 = 2^1 * 3^2
Therefore number of factors of 18 = (1+1)*(2+1) = 6 = say A

{factors of 18 are (1,18) , (2,9) , (3,6) i.e 6 in number}

Now product of all factors of 18 = 18^(A/2) = 18^(6/2) = 18^3 = 5832 (Answer is E)
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Re: What is the product of all positive factors of 18?  [#permalink]

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New post 14 Mar 2016, 05:26
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Re: What is the product of all positive factors of 18?  [#permalink]

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New post 23 Oct 2016, 11:36
Bunuel wrote:
What is the product of all positive factors of 18?

A. 39
B. 324
C. 1521
D. 3042
E. 5832



all positive factor of 18 are:
18, 9, 6, 3, 2, and 1.
3*2 = 6.
6*6 = 36
18*9 = smth smth 2

36* smth smth 2 = last digit is 2.
A, B, C are out.


since we have 18 (has a factor of 2), then 6 (has another factor of two), then another 2. the number itself must contain at least 3 factors of two.
3042 /2 = 1521 - ouch, no more factors of two.

E is the answer.
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Re: What is the product of all positive factors of 18?  [#permalink]

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New post 23 Oct 2016, 13:54
mvictor wrote:

all positive factor of 18 are:
18, 9, 6, 3, 2, and 1.
3*2 = 6.
6*6 = 36
18*9 = smth smth 2

36* smth smth 2 = last digit is 2.
A, B, C are out.


since we have 18 (has a factor of 2), then 6 (has another factor of two), then another 2. the number itself must contain at least 3 factors of two.
3042 /2 = 1521 - ouch, no more factors of two.


E is the answer.


No issues with the approach, however the calculations ( in the highlighted part ) can be simplified -

18 x 9 ~ 18 x 10 = 180
180 x 6 = 1080
1080 x 3 = 3024
3024 x 2 = Will be Greater than option (D)

Hence answer will definitely be (E) :-D
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Re: What is the product of all positive factors of 18?  [#permalink]

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New post 24 Oct 2016, 05:39
Just Another Approach could be => The unit digit method
The unit digit of 1*2*3*6*9*18 => 2
so we know that D or E is the Answer.
Now D can't be the answer since 3042=2*9*13*13
and 13 is clearly not a prime factor of 18
hence E must be true
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Re: What is the product of all positive factors of 18?  [#permalink]

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New post 27 Sep 2018, 17:33
Bunuel wrote:
What is the product of all positive factors of 18?

A. 39
B. 324
C. 1521
D. 3042
E. 5832


The positive factors of 18 are:

1, 2, 3, 6, 9, 18

The product of the first 4 numbers in the list is 36 and the product of the last two is 162. Therefore, the product of all the numbers in the list is:

36 x 162 = 5,832

Answer: E
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Re: What is the product of all positive factors of 18? &nbs [#permalink] 27 Sep 2018, 17:33
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