Real Numbers and Properties

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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?

It helps in determining the quotient and remainder in a division Signup and view all the answers

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

It facilitates easy determination of the LCM of two positive integers Signup and view all the answers

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

False 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.

False 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.

False Signup and view all the answers

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

True Signup and view all the answers

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

True Signup and view all the answers

Real Numbers and Properties

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Questions and Answers

What is the significance of Euclid’s division algorithm?

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

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

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

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

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

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

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.

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

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

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