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**Today we will determine the prime factors of all the numbers through 50**

Prime Number – a number that has only two factors, itself and 1. Factor – a number that divides evenly into another. Composite number – a number that has more than two factors.

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**Definition Product Product – An answer to a multiplication problem.**

7 x 8 = 56 Product

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Definition Factor – a number that is multiplied by another to give a product. 7 x 8 = 56 Factors

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Definition Factor – a number that divides evenly into another. 56 ÷ 8 = 7 Factor

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**Remember you learned factors in 4th grade?**

What are the factors of 42? 6 & 7 6 x 7 = 42

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What are the factors? 42 ÷ 7 = 6 7 & 6 63 ÷ 9 = 7 9 & 7

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**7 Definition 7 is prime because the only numbers**

Prime Number – a number that has only two factors, itself and 1. 7 7 is prime because the only numbers that will divide into it evenly are 1 and 7.

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**Examples of Prime Numbers**

2, 3, 5, 7, 11, 13, 17, 19 Special Note: One is not a prime number.

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**8 Definition The factors of 8 are 1, 2, 4, 8**

Composite number – a number that has more than two factors. 8 The factors of 8 are 1, 2, 4, 8

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**Examples of Composite Numbers**

4, 6, 8, 9, 10, 12, 14, 15 Special Note: Every whole number from 2 on is either composite or prime.

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**Our Lonely 1 One is not a prime nor a composite number.**

It is not prime because it does not have exactly two different factors. It is not composite because it does not have more than 2 factors. Special Note: One is not a prime nor a composite number.

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**So the prime numbers are 2 and 3**

Definition Prime Factorization – A way to write a composite number as the product of prime factors. 2 x 2 x 3 = 12 So the prime numbers are 2 and 3

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**Why is it important to know about Prime Factorization?**

It will be in the CST. It helps you understand multiplication and division better. A prime number can only be divided by 1 or itself, so it cannot be factored any further! Every other whole number can be broken down into prime number factors. It is like the Prime Numbers are the basic building blocks of all numbers. What are other reasons to know the all the prime factors to 50?

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**Let’s “draw” some Prime factor trees!**

Steps! Write down the composite number. Choose factors that equal the composite number (not the number times 1) Keep breaking the number down until all you have are prime numbers! Remember to circle your prime numbers! Write down your prime numbers from smallest to greatest! 12 x 6 Prime! 2 x x 2, 2, & 3

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**Let’s “draw” some Prime factor trees!**

Steps! Write down the composite number. Choose factors that equal the composite number (not the number times 1) Keep breaking the number down until all you have are prime numbers! Remember to circle your prime numbers! Write down your prime numbers from smallest to greatest! 16 x 4 2 x 2 x x 2 2, 2, 2, & 2

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**Let’s “draw” some Prime factor trees!**

Steps! Write down the composite number. Choose factors that equal the composite number (not the number times 1) Keep breaking the number down until all you have are prime numbers! Remember to circle your prime numbers! Write down your prime numbers from smallest to greatest! 25 x 5 5 & 5

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**Let’s review what we learned!**

What are composite numbers? numbers that have more than two factors. What are prime numbers? a number that has only two factors, itself and 1. What is the prime factorization of 20?

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Prime and Composite Factors: – When 2 or more numbers are multiplied, each number is called a factor of the product Ex) 1 x 5 = 52 x 5 = 10 1 x 10 = 10.

Prime and Composite Factors: – When 2 or more numbers are multiplied, each number is called a factor of the product Ex) 1 x 5 = 52 x 5 = 10 1 x 10 = 10.

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