Prime Numbers and Prime Factorization

🎬 Video: Prime Factorization Explained

What Are Prime Numbers? (0:01)

🌟 Definition of Prime numbers:

Prime numbers are natural numbers that have exactly two different factors: 1 and the number itself.

  • 2 is a prime number because it has only two factors: 1 and 2.
  • ❌ 4 is not a prime number because it has three factors: 1, 2, and 4.
  • ❌ 1 is not a prime number because it only has one factor: 1.

Exam tip: 2 is the smallest and only even prime number.

What are Common Prime Numbers? (0:46)

🧱 Prime numbers are often called the “building blocks” of mathematics because every whole number can be made by multiplying primes.

🌟 Prime Numbers Below 20 Are:

$$2,\ 3,\ 5,\ 7,\ 11,\ 13,\ 17,\ 19$$

🌟 Non-Prime Numbers Below 20 Are:

$$1,\ 4,\ 6,\ 8,\ 9,\ 10,\ 12,\ 14,\ 15,\ 16,\ 18 $$


Exam tip: Try to memorise the prime numbers; they show up a lot in maths exams, especially in questions about factors and multiples.

How to Do Prime Factorization Step by Step (0:58)

🌟 What Does Prime Factorization Mean?

Prime factorization means writing a number as a product of prime numbers only.

One method is using division.


🌟 Example of Prime Factorization:

Let’s factorise 90 step by step:

  • Start with the smallest prime number (2) that divides 90:

    $$90 = 2 \times 45$$

  • Try dividing 45 by the next smallest prime (3):

    $$ 90 = 2 \times 3 \times 15 $$

  • 15 is not a prime number, so we keep dividing:

    $$ 90 = 2 \times 3 \times 3 \times 5$$

  • All the numbers are now prime. So the final answer in index form is:

$$ 90 = 2 \times 3^2 \times 5 $$

How to Use a Factor Tree for Prime Factorization (2:19)

🌟 What Is A Factor Tree?

A factor tree is a visual method to break a number down into its prime factors step by step.


🌟 Example of Prime Factorisation:

Let’s start with 126.

  • Start with the smallest prime number (2):
    $$126 = 2 \times 63$$

  • Continue factoring the next number (3):
    $$63 = 3 \times 21$$

  • 21 is not a prime number, so we continue dividing: 
    $$21 = 3 \times 7$$

  • Now, all factors are prime numbers:
    $$126 = 2 \times 3 \times 3 \times 7$$

  • The Final answer in index form:
    $$126 = 2 \times 3^2 \times 7$$


Exam tip: This method helps you see the breakdown clearly and is especially useful for math exams.

📂 Flashcards: Prime Numbers and Prime Factorization

🍪 Quiz: Test Your Prime Factorization Skills

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