Home
Class 12
MATHS
Find the exponent of 3 in 100!....

Find the exponent of 3 in 100!.

Text Solution

Verified by Experts

In terms of prime factors 100! Can be written as `2^(a)*3^(b)*5^(c)*7^(d)`
Now, `b=E_(3)(100!)`
`=[(100)/(3)]+[(100)/(3^(4))]+[(100)/(3^(3))]+[(100)/(3^(4))]` + . . .
`=33+11+3+1+0+ . . .=48`
Hence, exponent of 3 is 48.
Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise JEE Type Solved Examples: Single Matching Type Questions|1 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise Exercise For Session 1|11 Videos

  • PARABOLA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

  • PROBABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|55 Videos

Similar Questions

Explore conceptually related problems

Find the exponent of 80 in 200!.

The exponent of 12 in 100! is

The exponent of 7 in 100C_50 is

Find five more such examples where a number is expressed in exponential form. Also identify the base and the exponent in each case. 4^(3)

Find five more such examples where a number is expressed in exponential form. Also identify the base and the exponent in each case. 8^(3)

Find five more such examples where a number is expressed in exponential form. Also identify the base and the exponent in each case. 2^(5)

Find five more such examples where a number is expressed in exponential form. Also identify the base and the exponent in each case. 5^(2)

Find five more such examples where a number is expressed in exponential form. Also identify the base and the exponent in each case. 7^(5)

Find the component of the following compound statements 100 is divisible by 3,11 and 5

Find the mean age of 100 residents of a colony from the following data :

ARIHANT MATHS-PERMUTATIONS AND COMBINATIONS -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Find the exponent of 3 in 100!.

    Text Solution

    |

  2. There is a rectangular sheet of dimension (2m-1)xx(2n-1), (where m > 0...

    Text Solution

    |

  3. If the letters of the word SACHIN are arranged in all possible ways ...

    Text Solution

    |

  4. lf r, s, t are prime numbers and p, q are the positive integers such t...

    Text Solution

    |

  5. At an election, a voter may vote for any number of candidates not grea...

    Text Solution

    |

  6. The letters of the word COCHIN are permuted and all the permutation...

    Text Solution

    |

  7. The set S""=""{1,""2,""3,""........ ,""12) is to be partitioned into...

    Text Solution

    |

  8. Consider all possible permutations of the letters of the word ENDEANOE...

    Text Solution

    |

  9. The number of words can be formed with the letters of the word 'MATHEM...

    Text Solution

    |

  10. In a shop, there are five types of ice-creams available. A child buys ...

    Text Solution

    |

  11. The number of seven digit integers, with sum of the digits equal to 10...

    Text Solution

    |

  12. Three boys and two girls stand in a queue. The probability that the nu...

    Text Solution

    |

  13. There are two urns. Urn A has 3 distinct red balls and urn B has 9 ...

    Text Solution

    |

  14. In how many ways 5 different balls can be distributed into 3 boxes so ...

    Text Solution

    |

  15. There are 10 points in a plane, out of these 6 are collinear. The numb...

    Text Solution

    |

  16. The total number of ways in which 5 balls of differert colours can be ...

    Text Solution

    |

  17. Let n denote the number of all n-digit positive integers formed by the...

    Text Solution

    |

  18. Let a(n) denote the number of all n-digit numbers formed by the digits...

    Text Solution

    |

  19. Assuming the balls to be identical except for difference in colours, t...

    Text Solution

    |

  20. Let Tn be the number of all possible triangles formed by joining ve...

    Text Solution

    |

  21. Consider the set of eight vector V={a hat i+b hat j+c hat k ; a ,bc in...

    Text Solution

    |