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## Euclid's Algorithm Multiple choice Questions and Answers (MCQs)

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Question 1 |

Euclid's algorithm is used for finding .....

GCD of two numbers | |

GCD of more than three numbers | |

LCM of two numbers | |

LCM of more than two numbers |

Question 1 Explanation:

Euclid's algorithm is basically used to find the GCD of two numbers. It cannot be directly applied to three or more numbers at a time.

Question 2 |

Who invented Euclid's algorithm?

Sieve | |

Euclid | |

Euclid-Sieve | |

Gabriel lame |

Question 2 Explanation:

Euclid invented Euclid's algorithm. Sieve provided an algorithm for finding prime numbers. Gabriel lame proved a theorem in Euclid's algorithm.

Question 3 |

If 4 is the GCD of 16 and 12, What is the GCD of 12 and 4?

12 | |

6 | |

4 | |

2 |

Question 3 Explanation:

Euclid's algorithm states that the GCD of two numbers does not change even if the bigger number is replaced by a difference of two numbers. So, GCD of 16 and 12 and 12 and (16-12)=4 is the same.

Question 4 |

Which of the following is not an application of Euclid's algorithm?

Simplification of fractions | |

Performing divisions in modular arithmetic | |

Solving quadratic equations | |

Solving diophantine equations |

Question 4 Explanation:

Solving quadratic equations is not an application of Euclid's algorithm whereas the rest of the options are mathematical applications of Euclid's algorithm.

Question 5 |

The Euclid's algorithm runs efficiently if the remainder of two numbers is divided by the minimum of two numbers until the remainder is zero.

True | |

False |

Question 5 Explanation:

The Euclid's algorithm runs efficiently if the remainder of two numbers is divided by the minimum of two numbers until the remainder is zero. This improvement in efficiency was put forth by Gabriel Lame.

There are 5 questions to complete.