Podcast
Questions and Answers
What does Euclid's division algorithm state about a positive integer a?
What does Euclid's division algorithm state about a positive integer a?
- It can be divided by a positive integer *b* leaving a remainder smaller than *b*. (correct)
- It cannot be divided by another positive integer.
- It can leave a remainder greater than *b*.
- It can be evenly divided by any positive integer.
Which of the following best describes the remainder r in Euclid's division algorithm?
Which of the following best describes the remainder r in Euclid's division algorithm?
- It is smaller than *b*. (correct)
- It is always zero.
- It is always equal to *b*.
- It can be greater than *b*.
What is a necessary condition for applying Euclid's division algorithm?
What is a necessary condition for applying Euclid's division algorithm?
- Both integers *a* and *b* must be even.
- The integer *a* must be less than *b*.
- The integer *a* must be greater than *b*. (correct)
- Both integers *a* and *b* must be irrational.
What is the primary focus of the sections following the introduction of real numbers?
What is the primary focus of the sections following the introduction of real numbers?
In the context of Euclid's division algorithm, what is meant by 'divisibility of integers'?
In the context of Euclid's division algorithm, what is meant by 'divisibility of integers'?
Study Notes
Chapter Overview
- This chapter continues the exploration of real numbers that began in Class IX, focusing on two key properties: the Euclid's division algorithm and the Fundamental Theorem of Arithmetic.
- The chapter begins by introducing the concept of divisibility of integers.
- Euclid's division algorithm states that any positive integer a can be divided by another positive integer b (where a is greater than b) leaving a remainder r that is smaller than b.
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Description
This quiz covers the properties of real numbers introduced in Class IX, specifically focusing on Euclid's division algorithm and the Fundamental Theorem of Arithmetic. It starts with the concept of divisibility of integers and explains how any positive integer can be divided by another, producing a remainder. Test your understanding of these key properties!
