Latest CAT Aptitude Question SOLUTION: n is a number such that 2n has 28 factors and 3n has 30 factors. then how many factors will 6n have?

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n is a number such that 2n has 28 factors and 3n has 30 factors.
then how many factors will 6n have?

Asked In CAT prabhav jain (8 years ago)

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Sakshi Agarwal  (8 years ago)

2n has 28 factors.
No of factors of a^p*B^q = (P+1)(q+1)....
28=4*7=(3+1)(6+1) ie. 2n= (3^3)*(2^6)

3n has 30 factors
30=5*6=(4+1)(5+1) ie 3n=(3^4)*(2^5)

Above values of 2n and 3n indicate that
n=(2^5)*(3^3)
»6n=(2^6)*(3^4)
Therefore, number of factors of 6n= (6+1)(4+1)=35

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Mukesh  (8 years ago)

LCM (28,30) = 420

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navya sri  (8 years ago)

here 2n has 28 factors and 3n has 30 factors so 6n =2n*3n so 28*30 factors are possible but here repititative factors should be removed.so by taking L.C.M the repititative factors are removed so ans is 2*14*15 i.e 420

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