# How many factors of x = 27 x 54 x 78 are there which are neither the factors of y = 23 x 52 x 75, nor of z = 25 x 53 x 73? Option 1) Option 2) Option 3) Option 4) Option 5)

$2^{7}*5^{4}*7^{8}$

Total number of factors$= 8*5*9=360$

Factors of$2^{3}*5^{2}*7^{5}=72$

Factors of$2^{5}*5^{3}*7^{3}=96$

Factors of$2^{3}*5^{2}*7^{3}=48$

Number of factors which are either factor of$2^{3}*5^{2}*7^{5} , 2^{5}*5^{3}*7^{3}, 2^{3}*5^{2}*7^{3}$

$72+96-48=120$

Number of factors which are neither factor of $2^{3}*5^{2}*7^{5} , 2^{5}*5^{3}*7^{3}$

$360-120=240$

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