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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)

    2

  • Option 2)

    230

  • Option 3)

    256

  • Option 4)

    None\: of \: these

  • Option 5)

    104

Answers (1)

best_answer

              2^{7}*5^{4}*7^{8}

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

Factors of2^{3}*5^{2}*7^{5}=72

Factors of2^{5}*5^{3}*7^{3}=96

Factors of2^{3}*5^{2}*7^{3}=48

Number of factors which are either factor of2^{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

Posted by

rishi.raj

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