Factorization for 8th Graders: Visual and Easy to Grasp

Welcome to understanding factorization! Today we'll learn how to break numbers into their building blocks.Let's start with the number twelve. We can arrange twelve blocks in a three by four array.This shows us that three times four equals twelve. Three and four are factors of twelve.Let's look at fifteen. We can arrange fifteen dots in a three by five array.Three times five equals fifteen. Three and five are the factors of fifteen.Think of factors as building blocks. When we multiply them together, they create a larger number.Factorization is like reverse multiplication. We start with the big number and find the smaller numbers that multiply to make it.To find all factors of a number systematically, we can use the division method.Let's start by dividing 24 by 1 and work our way up.When we divide by 2, we get 12. Both 2 and 12 are factors.Dividing by 3 gives us 8. Add these to our list of factors.When we divide by 4, we get 6. Both are factors of 24.We can organize these results as factor pairs.But how do we know when to stop looking for more factors?The square root of 24 is approximately 4.9. This means we only need to check divisors up to 4.Here's a systematic approach to finding all factors of a number.Now that we understand how to find factors systematically, we're ready to learn about prime factorization.Let's break down 36 into its prime factors using a factor tree.First, we can split 36 into any factor pair. Let's use 6 times 6.Now we break down each 6 into its prime factors: 2 times 3.So the prime factorization of 36 is 2 times 2 times 3 times 3.Now let's see how prime factorization helps us find the Greatest Common Factor of 36 and 24.We write out the prime factorization of both numbers.The Greatest Common Factor includes all prime factors that appear in both numbers. Here, that's two 2s and one 3, giving us 12.Similarly, we can find the Least Common Multiple using prime factorization.For the LCM, we use each prime factor the greatest number of times it appears in either number.So we need three 2s and two 3s, giving us 72 as our Least Common Multiple.Let's review what we've learned about prime factorization.Thanks for learning about prime factorization with Spark.E!