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Math for Kids23 chapters | 325 lessons

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Lesson Transcript

Instructor:
*Bethany Calderwood*

Bethany has taught special education in grades PK-5 and has a master's degree in special education.

Factorization is the process of breaking a number into its most basic parts. In this lesson, learn the definition of factors, prime numbers, and prime factors. We'll use a factor tree to find the prime factorization of a number.

Have you ever had a Boston cream donut? It's made of a cakey outside with cream inside and chocolate frosting on top. The cake, cream, and frosting are the parts of the donut. But those parts can be broken down into smaller ingredients, like flour, sugar, and yeast. Like the Boston cream donut, a number can be broken down into smaller parts. The smaller numbers that are multiplied together to form a number are called **factors**. Factors are the ingredients of a number.

Let's look at the number 32. We can multiply 4 times 8 to get 32, so 4 and 8 are factors of 32. But 4 and 8 are like the frosting and the cream in the donut; they are parts, but they are not the smallest possible parts. The numbers 4 and 8 can each be divided evenly by another number: the number 2. The 2 is a **prime number**, a number divisible only by 1 and itself. That means 2 is a prime factor of 32. A **prime factor** is a factor that is also a prime number. In other words, it's one of the smallest components of the number, and it can only be divided by 1 and by itself.

When trying to determine the basic ingredients of a donut, we look at the recipe. When trying to determine the basic ingredients of a number, the prime factors, we can make a factor tree. Look at this picture of the factor tree for 32.

The first branch shows that 32 is equal to 4 times 8. The next branch shows that 4 is equal to 2 times 2. Both these numbers are prime numbers, so this branch is finished. The 8 is broken into 2 times 4. Since 2 is a prime number, its branch is done. The 4 is broken into 2 times 2. Now all the numbers on the ends are prime. When we look at the circled numbers, we see all the prime factors of 32. The prime factorization of 32 is 2 x 2 x 2 x 2 x 2.

Here's another example for the number 40.

The first branch shows that 40 is equal to 4 times 10. Neither of these are prime numbers, so we keep going. The next branch breaks 4 into 2 times 2. Both of these are prime numbers. The 10 is broken into 2 times 5. Both of these are prime numbers. The prime factorization of 40 is 2 x 2 x 2 x 5.

You can start your factor tree in different ways. Here are some ideas:

- You can begin with a familiar multiplication fact.
- If the number is even, you can begin by dividing by 2.
- If the number ends in 5 or 0, you can begin by dividing by 5.
- If the sum of a number's digits is a number divisible by 3, you can begin by dividing by 3.

Once you have your first branch of the tree, circle any prime numbers. Continue to break down any numbers that are not prime. When every branch ends in a prime number, you have found the number's prime factorization.

The **factors** of a number are numbers that evenly divide into it. A **prime factor** is a factor that is only divisible by 1 and itself. You can use a factor tree to help you find a number's prime factorization.

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Math for Kids23 chapters | 325 lessons

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