If a factor of the number 2^33^55^27^4 is selected at random. What is

Question

If a factor of the number  2^33^55^27^4  is selected at random. What is the probability that it is odd?

A.  \frac{1}{3}

B.  \frac{1}{4}

C.  \frac{1}{2}

D.  \frac{6}{13}

E.  \frac{11}{14}

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CareerGeek · Accepted Answer

Let N =  2^33^55^27^4 
Total factors of N =  (3 + 1)*(5 + 1)*(2 + 1)*(4 + 1) = 4*6*3*5

Odd factors of N is same as total factors of  3^55^27^4  =  (5 + 1)*(2 + 1)*(4 + 1) = 6*3*5

Probability of Odd factors =  \frac{6*3*5}{4*6*3*5} = \frac{1}{4}

IMO Option B

LevanKhukhunashvili · Answer

Total Factors: 4*6*3*5=360
Dismiss prime two from the set to get only odd factors: 6*3*5=90

So the prob to pick only odd is  \frac{90}{360}=\frac{1}{4}

IMO
Ans:  B

bbb123 · Answer

From 2^3 * 3^5 * 5^2 * 7^4
Total factor = 3+5+2+4 (sum of every exponent) = 14
Odd factor = 5+2+4 (sum of odd exponent) = 11
So, prob. of odd factor = 11/14
Ans E

AdityaHongunti · Answer

Bunuel   chetan2u

Why aren't we accounting for repeats? There are 6 3's ...

So aren't we counting more than once..and hence need to account for it?i.e. divide the answer

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chetan2u · Answer

Hi

When you talk of 3^5 and we taking (5+1) or six 3s, it does not repeat anything 
The 6 3s mean  3^0, 3^1, 3^2, 3^3, 3^4 \ \ and \ \ 3^5.

Solution 
 2^3*3^5*5^2*7^4 
So odd factors will be given by  3^5*5^2*7^4........(5+1)(2+1)(4+1)=6*3*5 
Total factors =(3+1)*6*3*5
Probability of odd factors = \frac{6*3*5}{(4*6*3*5)}=\frac{1}{4}

So what is happening here is the probability is just dependent on the power of even number. 
Because each odd factor can be multiplied by 2^1 or 2^2 or 2^3, so 3 of them
Thus each odd factor leads to 3 more even factors, thus probability is  \frac{1*odd}{(1*odd+3*even)}=\frac{1}{4}

AdityaHongunti · Answer

Aah!! Silly mistake... I couldn't recognise that all the powers of 3 are in fact different numbers... Thank you so much !

mlahiq · Answer

Why did you guys add 1 to each number if the individual number of the factors?

If a factor of the number 2^33^55^27^4 is selected at random. What is

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If a factor of the number 2^33^55^27^4 is selected at random. What is

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