Fundamental Theorem of Arithmetic

The video tutorial explores the concepts of prime and composite numbers, emphasizing the importance of prime factorization. It introduces the fundamental theorem of arithmetic, which states that every composite number can be uniquely expressed as a product of prime numbers. The tutorial also demonstrates how to calculate the highest common factor (HCF) and least common multiple (LCM) using prime factorization. Additionally, it discusses interesting facts and exceptions related to the theorem, such as its inapplicability to the number one.

What are the basic building blocks of all natural numbers?

• Composite numbers

• Prime numbers

• Odd numbers

• Even numbers

What does the fundamental theorem of arithmetic state about composite numbers?

• They can be expressed as a product of primes.

• They can be expressed as a sum of primes.

• They can be expressed as a quotient of primes.

• They can be expressed as a difference of primes.

How can the number 70 be factorized according to the fundamental theorem of arithmetic?

• 2 * 5 * 7

• 7 * 5 * 2

• 5 * 7 * 2

• All of the above

What remains consistent in different ways of factorizing a number?

• The sum of factors

• The number of factors

• The prime factors

• The order of factors

What is the relationship between the product of HCF and LCM of two numbers?

• It is equal to the product of the numbers.

• It is equal to the difference of the numbers.

• It is equal to the sum of the numbers.

• It is equal to the quotient of the numbers.

How is the HCF of two numbers determined using prime factorization?

• By multiplying all prime factors

• By subtracting each common factor with the smallest power

• By adding all prime factors

• By multiplying each common factor with the smallest power

Why is the fundamental theorem of arithmetic not applicable to the number one?

• Because one is a prime number

• Because one is not a composite number

• Because one is an even number

• Because one is an odd number