How many odd factors does 210 have?

Question

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

chetan2u · Accepted Answer

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

rockstar23 · Answer

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!

sterling19 · Answer

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.

jaxndaxt145 · Answer

IMO E

210=1*2*3*5*7
can be expanded to 1,3, 5, 7, 15 ,21, 35, 105 }8 unique odd factors

PareshGmat · Answer

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

EMPOWERgmatRichC · Answer

Hi rockstar23,

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

GMAT assassins aren't born, they're made,
Rich

DesiGmat · Answer

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

OptimusPrepJanielle · Answer

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: https://www.optimus-prep.com/gmat-on-demand-course

Bunuel · Answer

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.

Divyadisha · Answer

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

Shiv2016 · Answer

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

AkshdeepS · Answer

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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How many odd factors does 210 have?

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How many odd factors does 210 have?

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