Prime Factorization

Exploring Prime Factorization and Factor Trees

Hey students! Today we're going to dive into a cool math concept called prime factorization. Imagine you have a number, say 60 and you want to break it down into only prime numbers. These prime numbers are the building blocks of 60. Using prime factorization, we find out that 60 can be broken down into 2² × 3 × 5. That means 60 is made up of two 2s, one 3, and one 5 all multiplied together.

Now, let's make this fun by drawing what we call a "factor tree." Start with 60 at the top, draw branches for each division by a prime number and keep going until you only have prime numbers at the ends. You’ll end up with a mini tree showing how 2, 3 and 5 come together to make 60. This helps us see everything clearly and makes it easier to understand.

Using Prime Factorization for Real Math Challenges

Alright, let’s put our new skill to the test. How can we use prime factorization to solve problems? It is helpful when we need to find the Least Common Multiple (LCM) or the Greatest Common Factor (HCF) of two numbers. Let’s take 24 and 36 as an example. First, break each number down using a factor tree:

24 is 2³ × 3
36 is 2² × 3²

To find the LCM, we take the highest power of all primes we see in the factorization. So for 24 and 36, the LCM is 2³ × 3² which equals 72. This is the smallest number both 24 and 36 can divide without leaving any remainder.

What about the HCF? It’s simpler than you think! Just take the lowest power for each prime number common to both numbers. So for 24 and 36, the HCF is 2² × 3 = 12. This number is the biggest one that can evenly divide both 24 and 36.

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