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**Prime and Composite Numbers, Prime Factorization, GCF & LCM.**

Prime Factors Prime and Composite Numbers, Prime Factorization, GCF & LCM.

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Checklist Points Understand the difference between a prime and composite number. You will be able to find the lowest common multiple and greatest common factor of a set of numbers.

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What are Factors?

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Prime Numbers A prime number is defined as a whole number which has exactly two factors. The two factors are always one and the number itself. Ex) What are the factors of 3, 7 and 11?

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Composite Numbers A composite number is a whole number which has more than two factors. Ex) What are the factors of 10 and 18? Note: the number 1 has only one factor and is neither prime nor composite

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Prime Factors The prime factors of a whole number are the factors of the number which are prime For example: The factors of 6 are 1, 2, 3, and 6. The prime factors of 6 are 2 and 3 ( because 1and 6 are not prime). DO: State the factors of 12. State the prime factors of 12.

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**[see Thiessen text pg 90 for more detail]**

Prime Factorization A composite number can be written as the product of its prime factors. This is called the prime factorization of the number. [see Thiessen text pg 90 for more detail] A small number can be factored in our heads but for larger numbers a tree diagram can be used.

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Factor Trees Find the prime factors of 48.

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Examples Find the prime factors of the following using the factor tree method. b) c) d)12

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**QUESTION: What is the difference between a factor and a multiple?**

GCF & LCM QUESTION: What is the difference between a factor and a multiple? Video: Factors and Multiples Give me an example of a factor of 15. Give me an example of a multiple of 15.

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**Greatest Common Factor**

The greatest common factor (GCF) of a set of whole numbers is the largest whole number which divides exactly into each of the numbers in the set. We will use our knowledge of prime factorization to determine the GCF of two numbers.

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**Steps to find GCF Factor each value using the factor tree.**

Circle the prime numbers that are common between the two numbers you are factoring. Multiply one set of those numbers to find your GCF Example:

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**Example #2 Find the greatest common factor of 48 and 64. **

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Example #3 Find the greatest common factor of 27, 90, 84.

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Least Common Multiple A common multiple is a number that is a multiple of two or more numbers. The common multiples of 3 and 4 are 12, 24, .... The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both. The least common multiple of 3 and 4 is 12. Ex) Multiples of 12 are… 12,24,36,48,60,72,…. Multiples of 18 are… 18,36,54,72,90,108,… The smallest multiple the 2 numbers have in common is the least common multiple, which is 36

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**Steps to Find LCM Factor each value using the factor tree.**

Write down the numbers they have in common only once (GCF), then write down the leftover numbers. Multiply them all together. **Easiest way to find the lcm is to use the chart shown in finding GCF

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Examples Find the greatest common factor and lowest common multiple of 2940 and 3150. Next Step: Put into chart

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**GCF: Factors that are common between both numbers**

LCM: Factors that are present in either/both numbers, but DO NOT DUPLICATE

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**Find the lowest common multiple between 22, 154, and 198**

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**Assignment 1) find the GCF of the following sets of numbers: a) 12, 3**

2) In the Thiessen textbook page 93, part C do the following questions: 1, 3, 6, 8, 9, 12

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