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AP EAMCET202316 May 2023Evening ShiftMathematicsBinomial TheoremActual

The greatest integer r such that 30^ r divides 30 ! is

Options

  1. A8
  2. B7
  3. C6
  4. D5

Correct answer

B. 7

Step-by-step solution

Since 30^ r divides 30 ! Now 30^ r =2^ r 3^ r 5^ r Since 5 divides 30 ! So r= [ 30 5 ]+ [ 30 5^2 ]=6+1=7

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