Quantitative Aptitude – Number system


Slot – 2 – Quantitative Aptitude – Number system – How many factors of 2^4 x 3^5

Q. How many factors of 2^4 x 3^5 x 10^4 are perfect squares which are greater than 1?

Answer: 44

Solution: 24 x 35 x 104 = 2^4×3^5×(2^4×5^4 )=2^8×3^5×5^4
Perfect square factors of the number will be of the form 2^a×3^b×5^c
Where a can be 0, 2, 4, 6 or 8 . b can be 0, 2 or 4 and c can be 0, 2 or 4
So total number of square factors = 5*3*3 = 45
But when a=b=c =0 factor will be 1.
Thus perfect squares which are greater than 1= 45 -1 = 44

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