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How many factors of 330 are odd numbers greater than 1?

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How many factors of 330 are odd numbers greater than 1?  [#permalink]

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New post 07 Sep 2016, 21:40
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A
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E

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How many factors of 330 are odd numbers greater than 1?
A. 3
B. 4
C. 5
D. 6
E. 7

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Re: How many factors of 330 are odd numbers greater than 1?  [#permalink]

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New post 08 Sep 2016, 00:16
When factorized, 330 has 4 prime factors. Of these prime factors 3 are odd and 1 is even. Hence total number of odd factors is 2*2*2(8), which includes 1. The total number of odd factors greater than 1 are 7.(option E)

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How many factors of 330 are odd numbers greater than 1?  [#permalink]

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New post 08 Sep 2016, 00:27
prime factors of 330 are 2^1,3^1,5^1 and 11^1
total divisors = (power if a prime factor+1)
total no. of odd factors(3,5,11) = (1+1)(1+1)(1+1) =8
since we need odd divisors other than 1 =>8-1 = 7 odd divisors

E is the answer
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Re: How many factors of 330 are odd numbers greater than 1?  [#permalink]

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New post 08 Sep 2016, 06:43
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MathRevolution wrote:
How many factors of 330 are odd numbers greater than 1?
A. 3
B. 4
C. 5
D. 6
E. 7

*An answer will be posted in 2 days.


330 is a pretty small #, so it wouldn't take long to LIST all of the odd factors.
We'll use the fact that 330 = (2)(3)(5)(11) AND the fact that ODD x ODD = ODD

So, the ODD factors of 330 are:
- 3
- 5
- 11
- (3)(5) [we need not evaluate this since we'll just going to count the factors in our list]
- (3)(11)
- (5)(11)
- (3)(5)(11)

Done!

Answer:

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Re: How many factors of 330 are odd numbers greater than 1?  [#permalink]

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New post 08 Sep 2016, 22:58
GMATPrepNow wrote:
MathRevolution wrote:
How many factors of 330 are odd numbers greater than 1?
A. 3
B. 4
C. 5
D. 6
E. 7

*An answer will be posted in 2 days.


330 is a pretty small #, so it wouldn't take long to LIST all of the odd factors.
We'll use the fact that 330 = (2)(3)(5)(11) AND the fact that ODD x ODD = ODD

So, the ODD factors of 330 are:
- 3
- 5
- 11
- (3)(5) [we need not evaluate this since we'll just going to count the factors in our list]
- (3)(11)
- (5)(11)
- (3)(5)(11)

Done!

Answer:

Nice! I did it this way too and I think it's very solid and intuitive. Yours is slicker though, I got the first 6 and then realized 330/2=165 for the last one. Your hint about not needing to follow through on the multiplication, and just listing the factors, is a huge time-saver for that.
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Re: How many factors of 330 are odd numbers greater than 1?  [#permalink]

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New post 10 Sep 2016, 20:31
If we calculate, we get 330=2*3*5*11. We are trying to find odd factors. So we have to find 3*5*11. From (1+1)(1+1)(1+1)=8, we only have to get rid of 1. The answer is 7. Hence, the correct answer is E.
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Re: How many factors of 330 are odd numbers greater than 1?  [#permalink]

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New post 06 Jan 2017, 19:01
Nice Question.
Here is my solution to this one ->
We need the odd factors of 330 greater than 1

330=2*5*3*11
For Odd factors => Power of 2 must be zero
Possible cases -> 1*2*2*2=>8
So 330 has 8 odd divisors including one.
Excluding one => 330 must have 7 odd divisors.
Hence E.
Perhaps a bigger trap can be when we include 8 in the options.

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Re: How many factors of 330 are odd numbers greater than 1?  [#permalink]

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