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What is the significance of Euclid’s division algorithm?
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?
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?
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?
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?
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.
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 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 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 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.
The long division process is a practical application of Euclid’s division algorithm.
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