Home
Class 10
MATHS
Explain Euclid's Division Lemma...

Explain Euclid's Division Lemma

Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    RD SHARMA ENGLISH|Exercise All Questions|390 Videos

  • SOME APPLICATIONS OF TRIGONOMETRY

    RD SHARMA ENGLISH|Exercise All Questions|154 Videos

Similar Questions

Explore conceptually related problems

State Euclid Division lemma

State Euclid Division lemma.

Find the HCF (865, 255) using Euclid’s division lemma

Theorem 1.1 (Euclid’s Division Lemma) : Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 ≤ r leq b.

Use Euclid's division lemma to show that the cube of any positive integer is of the form 9m , 9m+1 or 9m+8 .

Use Euclids division Lemma to show that the cube of any positive integer is either of the form 9m ,\ 9m+1 or, 9m+8 for some integer m .

Use Euclids division Lemma to show that the cube of any positive integer is either of the form 9m ,\ 9m+1 or, 9m+8 for some integer m .

Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m+1 for some integer m. [Hint: Let x be any positive integer then it is of the form 3q , 3q+1 or 3q+2 Now square each of these and sho

Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m+1 for some integer m.[Hint: Let x be any positive integer then it is of the form 3q , 3q+1 or 3q+2 Now square each of these and sho

Using Euclid's division algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3, respectively.

RD SHARMA ENGLISH-REAL NUMBERS-All Questions
  1. Explain Euclid's Division Lemma

    Text Solution

    |

  2. Three sets of English, Hindi and Mathematics books have to be stack...

    Text Solution

    |

  3. In a seminar. the number of participants in Hindi, English and Mathema...

    Text Solution

    |

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

    Text Solution

    |

  5. Find the HCF and LCM of 144, 180 and 192 by prime factorisation method...

    Text Solution

    |

  6. Explain why 7*11*13+13 and 7*6*5*4*3*2*1+5 are composite numbers.

    Text Solution

    |

  7. Prove that a positive integer n is prime number, if no prime p less th...

    Text Solution

    |

  8. Show that every positive even integer is of the form 2q, and that eve...

    Text Solution

    |

  9. prove that there are infinitely many positive integers.

    Text Solution

    |

  10. Determine the prime factorization of each of the following numbers: 13...

    Text Solution

    |

  11. Express each of the following positive integers as the product of its ...

    Text Solution

    |

  12. If a and b are two odd positive integers such that a > b, then prove t...

    Text Solution

    |

  13. Prove that one of every three consecutive positive integers is divi...

    Text Solution

    |

  14. Show that the square of an odd positive integer is of the form 8q+1, f...

    Text Solution

    |

  15. Prove that the square of any positive integer is of the form 5q ,5q+1,...

    Text Solution

    |

  16. Prove that if x and y are odd positive integers, then x^2+y^2 is even ...

    Text Solution

    |

  17. Show that one and only one out of n ,n+2 or n+4 is divisible by 3, whe...

    Text Solution

    |

  18. Prove that n^2-n divisible by 2 for every positive integer n.

    Text Solution

    |

  19. The remainder when the square of any prime number greater than 3 is ...

    Text Solution

    |

  20. Use Euclid’s division algorithm to find the HCF of 4052 and 12576.

    Text Solution

    |