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Questions and Answers
What is the result of Euclid’s division algorithm?
What is the result of Euclid’s division algorithm?
- It says any positive integer $a$ cannot be divided by another positive integer $b$.
- It says any positive integer $a$ can be divided by another positive integer $b$ in such a way that it leaves a remainder $r$ equal to $b$.
- It says any positive integer $a$ can be divided by another positive integer $b$ in such a way that it leaves a remainder $r$ that is smaller than $b$. (correct)
- It says any positive integer $a$ can be divided by another positive integer $b$ in such a way that it leaves a remainder $r$ that is greater than $b$.
What is the Fundamental Theorem of Arithmetic?
What is the Fundamental Theorem of Arithmetic?
- Every composite number can be expressed as a sum of primes in a unique way.
- Every prime number can be expressed as a sum of composites in a unique way.
- Every composite number can be expressed as a product of primes in a unique way. (correct)
- Every prime number can be expressed as a product of composites in a unique way.
What is the main application of the Fundamental Theorem of Arithmetic?
What is the main application of the Fundamental Theorem of Arithmetic?
- Computing the prime factorization of composite numbers. (correct)
- Finding the greatest common divisor (GCD) of two numbers.
- Solving quadratic equations.
- Computing the least common multiple (LCM) of two numbers.
What does the Fundamental Theorem of Arithmetic say about composite numbers?
What does the Fundamental Theorem of Arithmetic say about composite numbers?
How does Euclid’s division algorithm relate to finding the greatest common divisor (GCD) of two numbers?
How does Euclid’s division algorithm relate to finding the greatest common divisor (GCD) of two numbers?
What is the main application of Euclid’s division algorithm?
What is the main application of Euclid’s division algorithm?
What is the significance of the Fundamental Theorem of Arithmetic?
What is the significance of the Fundamental Theorem of Arithmetic?
In what way does Euclid’s division algorithm relate to finding the greatest common divisor (GCD) of two numbers?
In what way does Euclid’s division algorithm relate to finding the greatest common divisor (GCD) of two numbers?
What does the Fundamental Theorem of Arithmetic state about prime factorization?
What does the Fundamental Theorem of Arithmetic state about prime factorization?
How does Euclid’s division algorithm differ from the Fundamental Theorem of Arithmetic?
How does Euclid’s division algorithm differ from the Fundamental Theorem of Arithmetic?
What is the significance of the Euclid’s division algorithm and the Fundamental Theorem of Arithmetic in the field of mathematics?
What is the significance of the Euclid’s division algorithm and the Fundamental Theorem of Arithmetic in the field of mathematics?
How does the Euclid’s division algorithm relate to the computation of the highest common factor (HCF) of two positive integers?
How does the Euclid’s division algorithm relate to the computation of the highest common factor (HCF) of two positive integers?
Explain the concept of the Fundamental Theorem of Arithmetic and its uniqueness in expressing composite numbers as a product of primes.
Explain the concept of the Fundamental Theorem of Arithmetic and its uniqueness in expressing composite numbers as a product of primes.
What are the applications of the Euclid’s division algorithm and the Fundamental Theorem of Arithmetic in mathematics?
What are the applications of the Euclid’s division algorithm and the Fundamental Theorem of Arithmetic in mathematics?
How does the Euclid’s division algorithm differ from the Fundamental Theorem of Arithmetic in terms of their applications?
How does the Euclid’s division algorithm differ from the Fundamental Theorem of Arithmetic in terms of their applications?
