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How many odd factors does 210 have?

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

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New post 24 Feb 2015, 07:54
1
4
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

61% (00:36) correct 39% (00:28) wrong based on 252 sessions

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

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New post 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.
The correct answer is E.
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Re: How many odd factors does 210 have? [#permalink]

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New post 24 Feb 2015, 08:45
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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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New post Updated on: 26 Feb 2015, 10:24
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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.
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Re: How many odd factors does 210 have? [#permalink]

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New post 24 Feb 2015, 09:06
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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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New post 24 Feb 2015, 21:19
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Answer = E = 8

\(210 = 2^1 * 3^1 * 5^1 * 7^1\)

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

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New post 25 Feb 2015, 01:56
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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
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Re: How many odd factors does 210 have? [#permalink]

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New post 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.

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

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New post 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:

Start with the prime factorization: 210 = 2*3*5*7

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}

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

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New post 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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New post 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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New post 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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