What is Prime Factorization?
Prime factorization is like taking a number apart to see what prime numbers multiply together to make it!
Just like how a Lego castle is built from smaller blocks, every number is built from prime numbers. When we write this with exponents, we can show repeated multiplication in a neat, compact way.
How to Find Prime Factors with Exponents
1️⃣ Divide the number by the smallest prime number possible (start with 2!)
2️⃣ Keep dividing until you can't divide evenly anymore
3️⃣ Count how many times you used each prime number and write it as an exponent
Let's Try Some Examples!
Example 1: Factorize 24
Let's break down 24 into its prime factors step by step:
We divided by 2 three times and got one 3 at the end. So the prime factorization is:
24 = 2 × 2 × 2 × 3 = 23 × 31
Example 2: Factorize 72
Now let's try a bigger number. Can you find the prime factors of 72?
First, divide 72 by 2:
72 ÷ 2 = 36
Now factorize 36:
36 ÷ 2 = 18
Factorize 18:
18 ÷ 2 = 9
Now factorize 9:
9 ÷ 3 = 3
3 ÷ 3 = 1
72 = 2 × 2 × 2 × 3 × 3 = 23 × 32
Great job! You've broken 72 down into its prime building blocks!
Parent Tips 🌟
- Make it concrete: Use small objects like buttons or beans to physically group them into prime factors.
- Factor tree art: Turn prime factorization into an art project by creating colorful factor trees.
- Real-world connections: Show how prime factorization is used in computer security (like making passwords safe) to make it more relevant.