Take a minute and think about the following questions:
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Using multiplication o What is another way of saying 100? o Is there another way of saying your answer too? o Is there another way of saying that answer? o Is there another way of saying 101?
Write your thoughts in your notebook or discuss them with a neighbor.
Let’s see what our answers are to these questions.
Definitions:
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Factors o Whole numbers you multiply to produce another number
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Prime Number o A number with only two factors – 1 and itself
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Prime Factorization o The process of finding the prime numbers that multiply to produce another number
Let’s take a moment and try to brain storm as many prime numbers as we can. (Believe it or not, prime numbers are big business!!)

Consider 0 and 1:
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Do they have prime factors?
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Are they prime numbers?
Let’s take a few minutes and discuss these questions in groups and then we’ll see what we believe.
Examples:
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What are the factors for the number 12? o We need to know all the whole numbers that multiply to produce 12 so I’m going to list all the multiplications that give 12
1 x 12
2 x 6
3 x 4 o So 1, 2, 3, 4, 6 and 12 are the factors of 12.
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What are the prime factors of 12? o To do this we will use the process of prime factorization. o It is similar to what we just did to find the factors of 12. o One way is to start with the lowest prime numbers and divide the number by them until one works.
 Dividing by 1 doesn’t get anywhere so 2 is usually the first prime number to start at.
12 ÷ 2 = 6 o So we now have factors of 2 and 6. 2 is a prime number so we can’t go any further with it, but the 6 is not so we now

focus on dividing it by a prime number. We’ll use 2 again.
6 ÷ 2 = 3 o So for 6 we have factors of 2 and 3. o This means that for 12 we have prime factors of 2, 2 and 3 which we would write as
12 = 2 x 2 x 3 or 12 = 2 2 x 3 (prime-power factorization)
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What are the prime factors of 180? o Another way to tackle prime factorization is to start with multiplications you know. o I know 18 x 10 = 180 so all I’d need to do is the prime factorization of 18 and
10. o I’m using something called a factor tree to show my work this time. o This means that for 180 we have prime factors of 3, 2, 3, 5 and 2 so
180 = 2 x 2 x 3 x 3 x 5 or 180 = 2 2 x 3 2 x 5
Let’s try a few together:
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What are the factors of 144? (1-4, 6, 8, 9, 12, 16, 18, 24, 36, 48,
72, 144)
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What are the prime factors of 144? (3 2 , 2 4 )
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Write 540 as a product of its prime factors. Use a factor tree to show the breakdown of factors. (540 = 2 2 x 3 3 x 5)

Key Points:
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Neither 0 nor 1 is considered to have prime factors.
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There is only one unique set of prime factors for any number.
Try the question below on your own. If you can complete it correctly, you should be ready for the practice work.
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Write 504 as a product of its prime factors. (504 = 2 3 x 3 2 x 7)
Practice
Complete the Factors and Factorization Practice handout.