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Mastering Real Numbers

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Questions and Answers

Which property of positive integers is discussed in Sections 1.2 and 1.3 of the text?

Fundamental Theorem of Arithmetic

Irrational numbers

Euclid's division algorithm (correct)

Long division process

What does the Euclid's division algorithm state?

Any positive integer can be divided by another positive integer in such a way that it leaves a remainder equal to the divisor.

Any positive integer can be divided by another positive integer in such a way that it leaves a remainder smaller than the divisor. (correct)

Any positive integer can be divided by another positive integer without leaving any remainder.

Any positive integer can be divided by another positive integer in such a way that it leaves a remainder greater than the divisor.

What is the main application of the Euclid's division algorithm discussed in the text?

Computing the LCM of two positive integers

Computing the HCF of two positive integers (correct)

Computing the remainder of two positive integers

Computing the sum of two positive integers

What is the other important property of positive integers discussed in the text?

Fundamental Theorem of Arithmetic (D) Signup and view all the answers

What does the Fundamental Theorem of Arithmetic state?

Any positive integer can be expressed as a unique product of prime numbers. (A) Signup and view all the answers

What is the main application of the Euclid's division algorithm?

Computing the HCF of two positive integers Signup and view all the answers

What are the two important properties of positive integers discussed in this chapter?

Euclid's division algorithm and the Fundamental Theorem of Arithmetic Signup and view all the answers

What is the other name given to irrational numbers?

Real numbers Signup and view all the answers

What is the name of the result that states any positive integer can be divided by another positive integer in such a way that it leaves a remainder smaller than the divisor?

Euclid's division algorithm Signup and view all the answers

What is the topic of discussion in this chapter?