Overview
This lecture explains prime factors, demonstrates how to find them using factor trees, and covers expressing numbers as products of their prime factors.
Prime Factors Explained
- A prime factor is a factor of a number that is also a prime number.
- For example, factors of 12 are 1, 2, 3, 4, 6, 12, and the prime factors are 2 and 3.
- Exam questions may ask you to write a number as a product of its prime factors, meaning multiply prime numbers to get the original number.
Writing Numbers as Products of Prime Factors
- To write 12 as a product of its prime factors, use 2 × 2 × 3 = 12.
- Listing each prime factor as many times as it divides into the number is required.
Factor Trees Method
- Begin with the target number at the top, e.g., 220.
- Split the number into any two factors (e.g., 220 → 2 and 110).
- Circle any prime numbers; factorize non-primes further (e.g., 110 → 11 and 10).
- Continue until all branches end in prime numbers.
- Rewrite the number as a product of all circled prime numbers.
Example Factorizations
- For 220: 220 = 2 × 2 × 5 × 11, written as (2^2 × 5 × 11).
- For 112: 112 = 2 × 2 × 2 × 2 × 7, written as (2^4 × 7).
- The order of factorization does not change the final set of prime factors.
Prime Factorization Concept
- Prime factorization means expressing a number as the product of its prime factors.
- The term "express" in questions means to write or show the result.
Key Terms & Definitions
- Prime Number — a number with exactly two factors: 1 and itself.
- Factor — a number that divides another number with no remainder.
- Prime Factor — a factor that is also a prime number.
- Factor Tree — a diagram used to break down a number into its prime factors.
- Prime Factorization — expressing a number as a product of prime factors.
Action Items / Next Steps
- Practice prime factorization for different numbers using factor trees.
- Review homework or textbook exercises on prime factors and factor trees.