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FACTORS, MULTIPLES & PRIME NUMBERS GCF & LCM

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WHAT’S A FACTOR? A number that can be divided evenly into another number. Students will often identify multiples instead of factors. Students often miss a factor when listing them. Will divide evenly into only some greater numbers. There are a limited amount of factors for each number. Usually identified in pairs. Factor

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WHAT’S A MULTIPLE? A number that can be divided evenly by another number. Students will often identify factors instead of multiples. Every number has multiples There are an infinite amount of multiples for each number. Created by pairs of factors. Multiple Multiplication tables are just lists of multiples.

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WHAT’S A PRIME NUMBER? A number that can be divided only by itself and 1. Students often think odd numbers are prime numbers. Example: 9 Every number can be divided by a prime number. Prime numbers are the foundation of all numbers. Prime Number

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Makes All Types of Division Easier! Long Division Writing a number in lowest terms GCF LCM Distributive Property Simplify Fractions Solving Ratios Much More Divisibility Rules

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WHY USE PRIME NUMBERS? Just like houses are built from bricks… Composite numbers are built from prime numbers… So, we will use the prime numbers: 2, 3, 5 and sometimes 7… To break down composite numbers. 24 12 3 6 ÷ 2 2 2 1 3

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List all of the factors of 54: GREATEST COMMON FACTOR 2 1 6 3 18 9 27 54 If one number is a factor of the original number, all of its factors are factors of the original number, too! Ex: A peanut butter sandwich has peanut butter on it. Peanut butter has peanuts. Since peanut butter has peanuts and is on the peanut butter sandwich, the peanut butter sandwich has peanuts, too! Since 54 has a factor of 6, then the factors of 6 (1, 2, 3, 6) are factors of 54, too. Since 54 has the factors of 3 and 9, then the product of 3 & 9 (3 x 9 = 27) will create a factor of 54, too! Using that thinking, what other factor can you find? Enter it into your MathBerry. 6 x 3 = 18; 18 is a factor, too!

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What happens when we have to find factors for more than one number AND find the GCF? What happens, if we miss a factor? Do you really want to find factors that don’t matter? Let’s work smarter, not harder! Use prime numbers: (1)To find only the common factors (2)To find the correct greatest common factor. (3)Avoid making mistakes. GREATEST COMMON FACTOR

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First, let’s learn how to use the GCF Gold Digger! You will need the first four prime numbers: 2, 3, 5 & 7 GREATEST COMMON FACTOR

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The numbers you want to factor, go here! Now… think like a Gold Digger! Starting with the first prime number (2), can it divide evenly into both of the original numbers? (Hint: Use your divisibility rules!) If YES, put it here. The quotient of 2 goes below each dividend. DIG! Divide by 2 until you cannot divide by 2 anymore! If NO, move to the next prime number (3) and repeat! Once the dividends cannot be divided by any prime number, stop. 24 12 2 6 ÷ 2 3 2 36 18 9 3 GREATEST COMMON FACTOR

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Now that all common prime number factors have been found, use them to ‘build’ the Greatest Common Factor. 2 x 2 x 3 = 12 24 12 2 6 ÷ 2 3 2 36 18 9 3 GREATEST COMMON FACTOR GCF 4 x x 3 12 =

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The numbers you want to factor, go here! Now… think like a Gold Digger! Starting with the first prime number (2), can it divide evenly into both of the original numbers? (Hint: Use your divisibility rules!) If YES, put it here. The quotient of 2 goes below each dividend. DIG! Divide by 2 until you cannot divide by 2 anymore! If NO, move to the next prime number (3) and repeat! Once the dividends cannot be divided by any prime number, stop. 18 9 1 3 ÷ 3 3 2 90 45 15 5 GREATEST COMMON FACTOR

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Now that all common prime number factors have been found, use them to ‘build’ the Greatest Common Factor. 2 x 3 x 3 = 18 18 9 1 3 ÷ 3 3 2 90 45 15 5 GREATEST COMMON FACTOR GCF 6 x x 3 18 =

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The numbers you want to factor, go here! Now… think like a Gold Digger! Starting with the first prime number (2), can it divide evenly into both of the original numbers? (Hint: Use your divisibility rules!) If YES, put it here. The quotient of 2 goes below each dividend. DIG! Divide by 2 until you cannot divide by 2 anymore! If NO, move to the next prime number (3) and repeat! Once the dividends cannot be divided by any prime number, stop. 50 25 5 ÷ 5 2 90 45 9 GREATEST COMMON FACTOR

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Now that all common prime number factors have been found, use them to ‘build’ the Greatest Common Factor. 2 x 5 = 10 50 25 5 ÷ 5 2 90 45 9 GREATEST COMMON FACTOR GCF 10 x =

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Show your work on your white board and enter your answer into your MathBerries! 3 x 3 = 9 45 15 5 ÷ 3 3 99 33 11 NOW, YOU TRY! GCF 9 x 9=

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FACTORING SINGLE DIGIT NUMBERS ADDITIONAL WORK WITH SINGLE NUMBER FACTORING The following slides are not needed for this unit, but provide challenging work through application of prime numbers to factoring. Attention to detail is needed.

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(1) Find all prime number factors for the number. (2) List 1. (3) List each factor from the chart once. (4) Multiply each row across. 2 x 25 = 50 5 x 5 = 25 (5) Multiply as many combinations of the prime number factors from the chart, as you can to find any remaining composite factors. 2 x 5 = 10 5 x 5 = 25 50 25 5 ÷ 5 2 FACTORING USING PRIME NUMBERS

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24 12 6 ÷ 2 2 FACTORING USING PRIME NUMBERS 32 (1) Find all prime number factors for the number. (2) List 1. (3) List each factor from the chart once. (4) Multiply each row across. 2 x 12 = 24 2 x 6 = 12 2 x 3 = 6 (5) Multiply as many combinations of the prime number factors from the chart, as you can to find any remaining composite factors. 2 x 2 = 42 x 3 = 6 2 x 2 x 2 = 82 x 2 x 3 = 12 2 x 2 x 2 x 3 = 24

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36 18 9 ÷ 2 2 FACTORING USING PRIME NUMBERS 33 3 1 (1) Find all prime number factors for the number. (2) List 1. (3) List each factor from the chart once. (4) Multiply each row across. 2 x 18 = 36 2 x 9 = 18 3 x 3 = 9 3 x 1 = 3 (5) Multiply as many combinations of the prime number factors from the chart, as you can to find any remaining composite factors. 2 x 2 = 42 x 3 = 6 2 x 2 x 3 = 122 x 3 x 3 = 18 2 x 2 x 2 x 3 = 36

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18 9 3 ÷ 3 2 NOW, YOU TRY! (1) Find all prime number factors for the number. (2) List 1. (3) List each factor from the chart once. (4) Multiply each row across. 2 x 9 = 18 3 x 3 = 9 3 x 1 = 3 (5) Multiply as many combinations of the prime number factors from the chart, as you can to find any remaining composite factors. 2 x 3 = 6 3 x 3 = 9 2 x 3 x 3 = 18 3 1

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(1) Find all prime number factors for the number. (2) List 1. (3) List each factor from the chart once. (4) Multiply each row across. 2 x 45 = 903 x 15 = 45 3 x 5 = 155 x 1 = 5 (5) Multiply as many combinations of the prime number factors from the chart, as you can to find any remaining composite factors. 2 x 3 = 62 x 5 = 10 3 x 3 = 93 x 5 = 15 2 x 3 x 3 = 182 x 3 x 5 = 30 3 x 3 x 5 = 452 x 3 x 3 x 5 = 90 90 45 15 ÷ 3 2 NOW, YOU TRY! 53 5 1

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