Real Numbers and Properties
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Questions and Answers

What is the significance of Euclid’s division algorithm?

  • It helps in determining whether a number is prime or composite
  • It helps in computing the GCD of two positive integers (correct)
  • It helps in computing the LCM of two positive integers
  • It helps in simplifying algebraic expressions

    • What is the main application of the Fundamental Theorem of Arithmetic?

  • Solving linear equations involving integers
  • Expressing composite numbers as product of primes (correct)
  • Determining the divisibility of two positive integers
  • Computing the HCF of two positive integers

    • In the context of positive integers, what does the Fundamental Theorem of Arithmetic state?

  • Every prime number can be expressed as a product of positive integers
  • Every positive integer can be expressed as a product of any two primes
  • Every positive integer has only one factorization into primes
  • Every composite number can be expressed as a product of primes in a unique way (correct)

    • How does Euclid’s division algorithm relate to long division process?

    <p>It helps in determining the quotient and remainder in a division</p> Signup and view all the answers

    What is the significance of the unique factorization property mentioned in the Fundamental Theorem of Arithmetic?

    <p>It facilitates easy determination of the LCM of two positive integers</p> Signup and view all the answers

    Euclid’s division algorithm is mainly used to compute the LCM of two positive integers.

    <p>False</p> Signup and view all the answers

    The Fundamental Theorem of Arithmetic states that every composite number can be expressed as a product of primes in multiple ways.

    <p>False</p> Signup and view all the answers

    The remainder obtained when a positive integer a is divided by another positive integer b using Euclid’s division algorithm is always greater than b.

    <p>False</p> Signup and view all the answers

    The Fundamental Theorem of Arithmetic has deep and significant applications in the field of mathematics.

    <p>True</p> Signup and view all the answers

    The long division process is a practical application of Euclid’s division algorithm.

    <p>True</p> Signup and view all the answers

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