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How many odd factors does 210 have?

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Math Expert
Joined: 02 Sep 2009
Posts: 46207
How many odd factors does 210 have? [#permalink]

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24 Feb 2015, 07:54
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How many odd factors does 210 have?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

Kudos for a correct solution.

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Re: How many odd factors does 210 have? [#permalink]

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24 Feb 2015, 08:00
1
Making a factor pair table:

1 * 210
2 * 105
3 * 70
5 * 42
6 * 35
7 * 30
10 * 21
14 * 15

There are eight pairs and each pair has one odd factor.
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Re: How many odd factors does 210 have? [#permalink]

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24 Feb 2015, 08:45
1
IMO E

210=1*2*3*5*7
can be expanded to 1,3, 5, 7, 15 ,21, 35, 105 }8 unique odd factors
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How many odd factors does 210 have? [#permalink]

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Updated on: 26 Feb 2015, 10:24
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1
IMO E

Factors of 210 = 2 x 3 x 5 x 7.
Apart from 2, all remaining factors are odd and will produce odd results. So basically now the question becomes, find the number of factors of (3 x 5 x 7).

Using the formula we straight away get 8. No need to list down the factors at all!
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Originally posted by rockstar23 on 24 Feb 2015, 08:55.
Last edited by rockstar23 on 26 Feb 2015, 10:24, edited 1 time in total.
Math Expert
Joined: 02 Aug 2009
Posts: 5898
Re: How many odd factors does 210 have? [#permalink]

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24 Feb 2015, 09:06
2
Bunuel wrote:
How many odd factors does 210 have?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

Kudos for a correct solution.

ans 8...E
210= 2*3*5*7...
number of odd factors will be without 2.. so number of factors=(1+1)*(1+1)*(1+1)=8
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Re: How many odd factors does 210 have? [#permalink]

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24 Feb 2015, 21:19
1

$$210 = 2^1 * 3^1 * 5^1 * 7^1$$

Total factors = (1+1)(1+1)(1+1)(1+1) = 16

$$Odd factors = 2^3 = 8$$
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Re: How many odd factors does 210 have? [#permalink]

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24 Feb 2015, 23:19
rockstar23 wrote:
IMO D

Factors of 210 = 2 x 3 x 5 x 7.
Apart from 2, all remaining factors are odd and will produce odd results. So basically now the question becomes, find the number of factors of (3 x 5 x 7).

Using the formula we straight away get 8. No need to list down the factors at all!

Hi rockstar23,

Your approach is correct, but you've listed the wrong answer. A minor point, but an important one.

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Manager Joined: 27 Oct 2013 Posts: 237 Location: India Concentration: General Management, Technology GMAT Date: 03-02-2015 GPA: 3.88 Re: How many odd factors does 210 have? [#permalink] Show Tags 25 Feb 2015, 01:56 3 Here we go: 210 = 2 * 3 * 5 * 7 Odd factors(exclude 2) = 3^1 * 5^1 * 7^1 =====> (1+1) * (1+1) * (1+1) ----> 2 * 2 * 2 = 8 option E is correct To add ----> If someone is interested in finding out the number of even factors ---> {Total factor} - {Odd Factors} ---> 16 - 8 = 8 SVP Joined: 06 Nov 2014 Posts: 1888 Re: How many odd factors does 210 have? [#permalink] Show Tags 28 Feb 2015, 07:00 1 Bunuel wrote: How many odd factors does 210 have? (A) 3 (B) 4 (C) 5 (D) 6 (E) 8 Kudos for a correct solution. 210 = 2^1 * 3^1 * 5^1 * 7^1 We can see that all are odd numbers except 2. Multiplication with an even number yields an even number. Total factors = (1+1)(1+1)(1+1)(1+1) = 16 Out of these we only need to consider factors of 3,5, and 7 = (1+1)(1+1)(1+1) = 8 Hence option E. -- Optimus Prep's GMAT On Demand course for only$299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: http://www.optimus-prep.com/gmat-on-demand-course
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Re: How many odd factors does 210 have? [#permalink]

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02 Mar 2015, 06:27
Bunuel wrote:
How many odd factors does 210 have?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

For odd factors, we put aside the factor of two, and look at the other prime factors.
set of exponents = {1, 1, 1}
plus 1 to each = {2, 2, 2}
product = 2*2*2 = 8

Therefore, there are 8 odd factors of 210. In case you are curious, they are {1, 3, 5, 7, 15, 21, 35, and 105}

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Re: How many odd factors does 210 have? [#permalink]

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04 Jun 2016, 08:07
Bunuel wrote:
How many odd factors does 210 have?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

Kudos for a correct solution.

Opting out even factors from total number of factors will give total odd factors.

factors of 210= 5*2*7*3

If we do not consider factors of 2, we will get total odd factors= (1+1)(1+1)(1+1)= 2*2*2= 8
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Re: How many odd factors does 210 have? [#permalink]

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03 Sep 2017, 03:55
Any integer * Even integer = Even integer

Therefore we do not calculate number of factors of 2.

3^1*7*1*5*1

= (2*2*2)
=8
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Re: How many odd factors does 210 have? [#permalink]

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31 May 2018, 23:15
Bunuel wrote:
How many odd factors does 210 have?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

Kudos for a correct solution.

210 = 2 * 3 * 5 * 7

Odd factors will be without 2 as factor:

Add 1 to powers of 3,5,7:

2 * 2 * 2 = 8

(E)
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Re: How many odd factors does 210 have?   [#permalink] 31 May 2018, 23:15
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