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Let`s Learn: Prime Factorisation | Mathematics Class 8- New NCERT (Ganita Prakash)

The document Let's Learn: Prime Factorisation | Mathematics Class 8- New NCERT (Ganita Prakash) is a part of the Class 8 Course Mathematics Class 8- New NCERT (Ganita Prakash).
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FAQs on Let's Learn: Prime Factorisation - Mathematics Class 8- New NCERT (Ganita Prakash)

1. What is prime factorization and why is it important?
Ans.Prime factorization is the process of breaking down a composite number into the product of its prime factors. A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. Prime factorization is important because it helps in understanding the properties of numbers, simplifying fractions, and finding the greatest common divisor (GCD) and least common multiple (LCM) of numbers.
2. How can I find the prime factorization of a number?
Ans.To find the prime factorization of a number, you can use methods such as trial division, where you divide the number by the smallest prime number (2, 3, 5, etc.) and continue dividing until you reach 1. Alternatively, you can use a factor tree method, where you break the number down into factors and continue to factor each composite number until all factors are prime.
3. Can prime factorization be used for large numbers?
Ans.Yes, prime factorization can be used for large numbers, but it can be more complex and time-consuming. Methods like using algorithms or computer software can assist in finding the prime factorization of larger numbers efficiently. However, for educational purposes, smaller numbers are typically used to illustrate the concept.
4. What is the significance of the Fundamental Theorem of Arithmetic in relation to prime factorization?
Ans.The Fundamental Theorem of Arithmetic states that every integer greater than 1 can be expressed uniquely as a product of prime numbers, up to the order of the factors. This theorem underlines the importance of prime factorization because it assures that the prime factors of a number are consistent and provides a foundation for number theory.
5. How does prime factorization help in finding the GCD and LCM of two numbers?
Ans.Prime factorization helps in finding the greatest common divisor (GCD) and least common multiple (LCM) of two numbers by allowing you to compare their prime factors. The GCD can be found by multiplying the lowest powers of all common prime factors, while the LCM can be calculated by multiplying the highest powers of all prime factors present in both numbers. This systematic approach simplifies the process significantly.
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