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# How many different positive even integers are factors of 294?

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Math Expert
Joined: 02 Sep 2009
Posts: 50585
How many different positive even integers are factors of 294?  [#permalink]

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29 Dec 2016, 11:14
1
3
00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:47) correct 37% (01:40) wrong based on 154 sessions

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How many different positive even integers are factors of 294?

A. 4
B. 6
C. 7
D. 9
E. 11

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Math Expert
Joined: 02 Sep 2009
Posts: 50585
Re: How many different positive even integers are factors of 294?  [#permalink]

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12 Jan 2017, 08:45
1
4
KS15 wrote:
Is there a way to calculate the even factors and odd factors without listing?

Thanks

294 = 2*3*7^2.

The number of factors of 294 is (1 + 1)(1 + 1)(2 + 1) = 12.

Even factors come from 2's in the prime factorization of a number. So, to get the number of odd factors get rid of 2's. Thus the number of odd factors of 294 is the same as the number of odd factors of 3*7^2, which is (1 + 1)(2 + 1) = 6.

Now, to find the number of even factors subtract odd factors from the total number of factors --> 12 - 6 = 6.

Hope it's clear.
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Senior Manager
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: How many different positive even integers are factors of 294?  [#permalink]

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29 Dec 2016, 11:47
Bunuel wrote:
How many different positive even integers are factors of 294?

A. 4
B. 6
C. 7
D. 9
E. 11

$$294 = 2*3*7^2$$

# of even factors = 1*2*3 = 6

Answer B
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Location: Canada
Re: How many different positive even integers are factors of 294?  [#permalink]

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29 Dec 2016, 13:50
1
Top Contributor
Bunuel wrote:
How many different positive even integers are factors of 294?

A. 4
B. 6
C. 7
D. 9
E. 11

294 = (2)(3)(7)(7)

Since the answer choices are relatively small, let's list all of the EVEN factors:
- (2)
- (2)(3)
- (2)(7)
- (2)(7)(7)
- (2)(3)(7)
- (2)(3)(7)(7)

Answer: B
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Joined: 22 May 2015
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Re: How many different positive even integers are factors of 294?  [#permalink]

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29 Dec 2016, 18:34
2
1
294 = 2*3*7^2

Total factors - Odd Factors = 12(2*2*3) -6(2*3) =6
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Re: How many different positive even integers are factors of 294?  [#permalink]

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11 Jan 2017, 09:12
Is there a way to calculate the even factors and odd factors without listing?

Thanks
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Joined: 09 Sep 2013
Posts: 8774
Re: How many different positive even integers are factors of 294?  [#permalink]

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21 Mar 2018, 09:01
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Re: How many different positive even integers are factors of 294? &nbs [#permalink] 21 Mar 2018, 09:01
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# How many different positive even integers are factors of 294?

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