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How many different positive even integers are factors of 294?

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

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New post 29 Dec 2016, 11:14
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63% (01:47) correct 37% (01:40) wrong based on 154 sessions

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

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New post 12 Jan 2017, 08:45
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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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Re: How many different positive even integers are factors of 294?  [#permalink]

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New post 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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Re: How many different positive even integers are factors of 294?  [#permalink]

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New post 29 Dec 2016, 13:50
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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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Re: How many different positive even integers are factors of 294?  [#permalink]

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

Thanks
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Re: How many different positive even integers are factors of 294?  [#permalink]

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New post 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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