✔ Five is the only prime number in the list. Four, six, and eight are composite.
Q2. What does the theorem guarantee?
✔ The Fundamental Theorem states prime factorization is unique for every composite number.
Q3. Identify the error in 120 = 2^3 x 6 x 5.
✔ All factors must be prime. Six is composite and should be split into two and three.
Show transcript
[Slide 1] What is the Theorem?
Welcome students. This theorem states every composite number can be expressed as a product of primes uniquely. Think of primes as LEGO bricks for numbers.
[Slide 2] The Fundamental Statement
Mathematically, any number n equals primes raised to powers. The sequence of primes is unique regardless of arrangement. This forms the basis for finding HCF and LCM.
[Slide 3] Example: Factorizing 120
Let us factorize one hundred twenty. Divide by two three times, then by three and five. The final expression shows the unique prime factors.
[Slide 4] Avoid This Error
Students often stop at composite numbers like six. Remember, every factor must be a prime number. Also, do not skip writing the exponent one.
[Slide 5] Key Takeaways
Remember primes are the unique building blocks of numbers. The order of multiplication does not affect uniqueness. Apply this theorem to solve HCF problems easily.