Home
Class 10
MATHS
If the prime factorization of a natural ...

If the prime factorization of a natural number `n` is `2^3*3^2*5^2*6,` write the number of consecutive zeros in `ndot`

Text Solution

AI Generated Solution

To solve the problem, we need to find the number of consecutive zeros in the natural number \( n \) given its prime factorization. The prime factorization of \( n \) is \( 2^3 \times 3^2 \times 5^2 \times 6 \). ### Step-by-Step Solution: 1. **Understanding the Prime Factorization**: The prime factorization of \( n \) is given as: \[ n = 2^3 \times 3^2 \times 5^2 \times 6 ...
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    RD SHARMA|Exercise All Questions|390 Videos
  • SOME APPLICATIONS OF TRIGONOMETRY

    RD SHARMA|Exercise All Questions|154 Videos

Similar Questions

Explore conceptually related problems

Write the prime factorization of each number. 12

Write the prime factorization of each number. 80

If n=2^3xx3^4xx5^4xx7 , where n is a natural number, then find the number of consecutive zeros in n

Is 2^(3-n) a prime number for all natural numbers n?

The number of factors of a number N=2^(3)xx3^(2)xx5^(3) is

If [x] denotes the integral part of x and n is a natural number such that 1<=n<100 then the number of solutions of the equation [(n)/(2)]+[(n)/(3)]+[(n)/(5)]=(n)/(2)+(n)/(3)+(n)/(5) is

The sum of three consecutive odd natural numbers is 69. Find the prime number out of these numbers.

Prove that 7 is a factor of 2^(3n)-1 for all natural numbers n.

n^(3)-n is divisible by 6, for each natural numbers n ge2

If the average of 5 consecutive number starting with m is n. Find the average of 6 consecutive number starting with m + 2

RD SHARMA-REAL NUMBERS-All Questions
  1. There is a circular path around a sports field. Priya takes 18 minutes...

    Text Solution

    |

  2. A rectangular courtyard is 18m 72cm long and 13m 20cm broad. It is to ...

    Text Solution

    |

  3. If the prime factorization of a natural number n is 2^3*3^2*5^2*6, w...

    Text Solution

    |

  4. A circular field has a circumference of 360km. Three cyclists start ...

    Text Solution

    |

  5. In a morning walk three persons step off together, their steps measure...

    Text Solution

    |

  6. Prove that sqrt(2)+sqrt(5) is irrational.

    Text Solution

    |

  7. Show that there is no positive integer n for which sqrt(n-1)+sqrt(n+1...

    Text Solution

    |

  8. A merchant has 120 litres of oil of one kind, 180 litres of another ...

    Text Solution

    |

  9. Two brands of chocolates are available in packs of 24 and 15 respec...

    Text Solution

    |

  10. What is the largest number that divides 626, 3127 and 15628 and lea...

    Text Solution

    |

  11. Find the greatest number that will divide 445, 572 and 699 leaving ...

    Text Solution

    |

  12. Two tankers contain 850 litres and 680 litres of petrol respectively. ...

    Text Solution

    |

  13. Two sets of English and social science books containing 336 and 96 res...

    Text Solution

    |

  14. Find the HCF of 81 and 237 and express it as a linear combination of 8...

    Text Solution

    |

  15. Find the largest number that will divide 398, 436 and 542 leaving r...

    Text Solution

    |

  16. Let a,b,c,k be rational numbers such that k is not perfect cube if a ...

    Text Solution

    |

  17. Prove that for any prime positive integer p ,sqrt(p) is an irrational ...

    Text Solution

    |

  18. Let A B C D be a tetrahedron such that the edges A B ,A Ca n dA D a...

    Text Solution

    |

  19. 15 Pastries and 12 biscuit packets have been donated for a school fete...

    Text Solution

    |

  20. The length, breadth and height of a room are 8m and 25cm, 6m and 75m ...

    Text Solution

    |