Latest Elitmus Aptitude Question SOLUTION: sorry the question should be, How many factors of the number 2^5*3^4*5^2 are divisible by 12?

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(#M40019093) ELITMUS question Keep an EYE

sorry the question should be, How many factors of the number 2^5*3^4*5^2 are divisible by 12?

Asked In Elitmus Kishore Kumar (10 years ago)

Unsolved Read Solution (10)

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Sahil  (10 years ago)

48 is answer here is a shortcut write 12 = 2^2 * 3
we have (2^5 * 3^4 * 5^2) / (2^2 * 3) = 2^3 * 3^3 * 5^2

so to find no. of factors we have formula from theorem of divisibility that is to increase powers by 1 and multiply them

so answer is (3+1)*(3+1)*(2+1) = 48 answer

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babu rao ganpat rao apte  (10 years ago)

vinod...ur answer is wrong.... taking ur first case u didnt count 12 as a factor...moving on....4*9*25 or 4*9*5 ..... dude...u didnt count 4*9 as a factor....??? ...thus ur whole soln is wrong

correct answer::::: 48 if u count x^0 of every number

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vinod  (10 years ago)

2^5 * 3^4 * 5^2
----------------------------------
2 3 5
4 9 25
8 27
16 81
32


multiplying with different combinations; choosing those with 12 as one of multiplier we have to check each
for eg: 4*3*5
4*3*25
4*9*5
4*9*25
4*27*5
4*27*25
4*81*5
4*81*25
here 8 comb with '4'
in the same way do for, 8,16,32
ans
8+8+8+8=32

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venkatesh  (10 years ago)

2^5*3^4*5^2 = (2^2*3)*(2^3*3^3*5^2)
so the factors of 2^3*3^3*5^2 are (3+1)*(3+1)*(2+1) = 48 [power +1 ]
so total 48 factors

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Krishanu chatterjee  (10 years ago)

ans will be 7
because 2^5*3^4*5^2
will have (5+1)*(4+1)*(2+1) factors or
it is equal to=6*5*3=90
no of factors which r factors of 12 are=90/12=7.5
so it will be 7

Is this solution Helpfull? Yes (4) | No (25)  

prayas goel  (10 years ago)

Sum of all factors
(2^0+2^1+2^2+2^3+2^4+2^5)(3^0+3^1+3^2+3^3+3^4)(5^0+5^1+5^2)
No. of factors divisible by 12 means 2^2*3
In this case we have to take only this factors
(2^2+2^3+2^4+2^5)(3^1+3^2+3^3+3^4)(5^0+5^1+5^2)
mean
4*4*3 =48 factors Answer...

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SAMBIT KUMAR GHOSH  (10 years ago)

the number of factors of the given number is (5+1)*(4+1)*(2+1)= 90
now we will divide the number with 12 i.e 2^2*3^1=2^3*3^3*5^2,,now this immediate result has 48 factors.
so,the no of factors of the given number are divisible by 12 are (48+1)=49 ans

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Kishore Kumar  (10 years ago)

@krishanu... do not simply answer anything you like and click on yes... that is a wrong logic...12,24,48,36,60,72,96,108 etc are all factors of the number and are also divisible by 12

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SAMBIT KUMAR GHOSH  (10 years ago)

the answer shuld be (48+1)=49....coz we divide the number by 12 i.e 2^2*3
so we must have to add 1 at the time of result...so the ans will be 49.

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hemanth chowdary  (10 years ago)

gcrtsedbytg

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